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transition subsection</span> </button> <ul id="toc-Types_of_phase_transition-sublist" class="vector-toc-list"> <li id="toc-States_of_matter" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#States_of_matter"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>States of matter</span> </div> </a> <ul id="toc-States_of_matter-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Structural" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Structural"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Structural</span> </div> </a> <ul id="toc-Structural-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Magnetic" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Magnetic"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Magnetic</span> </div> </a> <ul id="toc-Magnetic-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mixtures" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mixtures"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Mixtures</span> </div> </a> <ul id="toc-Mixtures-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_examples" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Other_examples"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.5</span> <span>Other examples</span> </div> </a> <ul id="toc-Other_examples-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Classifications" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Classifications"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Classifications</span> </div> </a> <button aria-controls="toc-Classifications-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Classifications subsection</span> </button> <ul id="toc-Classifications-sublist" class="vector-toc-list"> <li id="toc-Ehrenfest_classification" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ehrenfest_classification"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Ehrenfest classification</span> </div> </a> <ul id="toc-Ehrenfest_classification-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Modern_classifications" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Modern_classifications"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Modern classifications</span> </div> </a> <ul id="toc-Modern_classifications-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Characteristic_properties" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Characteristic_properties"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Characteristic properties</span> </div> </a> <button aria-controls="toc-Characteristic_properties-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Characteristic properties subsection</span> </button> <ul id="toc-Characteristic_properties-sublist" class="vector-toc-list"> <li id="toc-Phase_coexistence" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Phase_coexistence"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Phase coexistence</span> </div> </a> <ul id="toc-Phase_coexistence-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Critical_points" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Critical_points"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Critical points</span> </div> </a> <ul id="toc-Critical_points-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Symmetry" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Symmetry"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Symmetry</span> </div> </a> <ul id="toc-Symmetry-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Order_parameters" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Order_parameters"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Order parameters</span> </div> </a> <ul id="toc-Order_parameters-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Relevance_in_cosmology" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Relevance_in_cosmology"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5</span> <span>Relevance in cosmology</span> </div> </a> <ul id="toc-Relevance_in_cosmology-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Critical_exponents_and_universality_classes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Critical_exponents_and_universality_classes"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.6</span> <span>Critical exponents and universality classes</span> </div> </a> <ul id="toc-Critical_exponents_and_universality_classes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Critical_phenomena" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Critical_phenomena"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.7</span> <span>Critical phenomena</span> </div> </a> <ul id="toc-Critical_phenomena-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Phase_transitions_in_biological_systems" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Phase_transitions_in_biological_systems"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.8</span> <span>Phase transitions in biological systems</span> </div> </a> <ul id="toc-Phase_transitions_in_biological_systems-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Phase_transitions_in_social_systems" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Phase_transitions_in_social_systems"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.9</span> <span>Phase transitions in social systems</span> </div> </a> <ul id="toc-Phase_transitions_in_social_systems-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Experimental" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Experimental"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Experimental</span> </div> </a> <ul id="toc-Experimental-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Phase transition</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 58 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-58" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">58 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D8%AD%D9%88%D9%84_%D8%B7%D9%88%D8%B1%D9%8A" title="تحول طوري – Arabic" lang="ar" hreflang="ar" data-title="تحول طوري" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Transici%C3%B3n_de_fase" title="Transición de fase – Asturian" lang="ast" hreflang="ast" data-title="Transición de fase" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Faza_ke%C3%A7idl%C9%99ri" title="Faza keçidləri – Azerbaijani" lang="az" hreflang="az" data-title="Faza keçidləri" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%A6%E0%A6%B6%E0%A6%BE%E0%A6%A8%E0%A7%8D%E0%A6%A4%E0%A6%B0" title="দশান্তর – Bangla" lang="bn" hreflang="bn" data-title="দশান্তর" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Si%C3%B2ng_cho%C3%A1n-%C3%AE" title="Siòng choán-î – Minnan" lang="nan" hreflang="nan" data-title="Siòng choán-î" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A4%D0%B0%D0%B7%D0%B0%D0%B2%D1%8B_%D0%BF%D0%B5%D1%80%D0%B0%D1%85%D0%BE%D0%B4" title="Фазавы пераход – Belarusian" lang="be" hreflang="be" data-title="Фазавы пераход" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A4%D0%B0%D0%B7%D0%BE%D0%B2_%D0%BF%D1%80%D0%B5%D1%85%D0%BE%D0%B4" title="Фазов преход – Bulgarian" lang="bg" hreflang="bg" data-title="Фазов преход" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Transici%C3%B3_de_fase" title="Transició de fase – Catalan" lang="ca" hreflang="ca" data-title="Transició de fase" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A4%D0%B0%D0%B7%C4%83%D0%BB%D0%BB%D0%B0_%D0%BA%D1%83%C3%A7%C4%83%D0%BC" title="Фазăлла куçăм – Chuvash" lang="cv" hreflang="cv" data-title="Фазăлла куçăм" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/F%C3%A1zov%C3%BD_p%C5%99echod" title="Fázový přechod – Czech" lang="cs" hreflang="cs" data-title="Fázový přechod" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Chirambo_(misandu)" title="Chirambo (misandu) – Shona" lang="sn" hreflang="sn" data-title="Chirambo (misandu)" data-language-autonym="ChiShona" data-language-local-name="Shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Phasen%C3%BCbergang" title="Phasenübergang – German" lang="de" hreflang="de" data-title="Phasenübergang" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Faasisiire" title="Faasisiire – Estonian" lang="et" hreflang="et" data-title="Faasisiire" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Transici%C3%B3n_de_fase" title="Transición de fase – Spanish" lang="es" hreflang="es" data-title="Transición de fase" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Faztransiro" title="Faztransiro – Esperanto" lang="eo" hreflang="eo" data-title="Faztransiro" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Fase-aldaketa" title="Fase-aldaketa – Basque" lang="eu" hreflang="eu" data-title="Fase-aldaketa" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%DA%AF%D8%B0%D8%A7%D8%B1_%D9%81%D8%A7%D8%B2" title="گذار فاز – Persian" lang="fa" hreflang="fa" data-title="گذار فاز" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Transition_de_phase" title="Transition de phase – French" lang="fr" hreflang="fr" data-title="Transition de phase" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gv mw-list-item"><a href="https://gv.wikipedia.org/wiki/Caghlaa_paase" title="Caghlaa paase – Manx" lang="gv" hreflang="gv" data-title="Caghlaa paase" data-language-autonym="Gaelg" data-language-local-name="Manx" class="interlanguage-link-target"><span>Gaelg</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%83%81%EC%A0%84%EC%9D%B4" title="상전이 – Korean" lang="ko" hreflang="ko" data-title="상전이" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%93%D5%B8%D6%82%D5%AC%D5%A1%D5%B5%D5%AB%D5%B6_%D5%A1%D5%B6%D6%81%D5%B8%D6%82%D5%B4" title="Փուլային անցում – Armenian" lang="hy" hreflang="hy" data-title="Փուլային անցում" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%B5%E0%A4%B8%E0%A5%8D%E0%A4%A5%E0%A4%BE_%E0%A4%B8%E0%A4%82%E0%A4%95%E0%A5%8D%E0%A4%B0%E0%A4%AE%E0%A4%A3" title="प्रावस्था संक्रमण – Hindi" lang="hi" hreflang="hi" data-title="प्रावस्था संक्रमण" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Fazni_prijelazi" title="Fazni prijelazi – Croatian" lang="hr" hreflang="hr" data-title="Fazni prijelazi" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Perubahan_wujud_zat" title="Perubahan wujud zat – Indonesian" lang="id" hreflang="id" data-title="Perubahan wujud zat" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Transition_de_phase" title="Transition de phase – Interlingua" lang="ia" hreflang="ia" data-title="Transition de phase" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Transizione_di_fase" title="Transizione di fase – Italian" lang="it" hreflang="it" data-title="Transizione di fase" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A2%D7%91%D7%A8_%D7%A4%D7%90%D7%96%D7%94" title="מעבר פאזה – Hebrew" lang="he" hreflang="he" data-title="מעבר פאזה" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A4%D0%B0%D0%B7%D0%B0%D0%BB%D1%8B%D2%9B_%D0%B0%D1%83%D1%8B%D1%81%D1%83" title="Фазалық ауысу – Kazakh" lang="kk" hreflang="kk" data-title="Фазалық ауысу" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/B%C5%ABsenos_kitimas" title="Būsenos kitimas – Lithuanian" lang="lt" hreflang="lt" data-title="Būsenos kitimas" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/F%C3%A1zis%C3%A1talakul%C3%A1s" title="Fázisátalakulás – Hungarian" lang="hu" hreflang="hu" data-title="Fázisátalakulás" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A4%D0%B0%D0%B7%D0%B5%D0%BD_%D0%BF%D1%80%D0%B5%D0%BC%D0%B8%D0%BD" title="Фазен премин – Macedonian" lang="mk" hreflang="mk" data-title="Фазен премин" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%85%E0%B4%B5%E0%B4%B8%E0%B5%8D%E0%B4%A5%E0%B4%BE%E0%B4%A8%E0%B5%8D%E0%B4%A4%E0%B4%B0%E0%B4%99%E0%B5%8D%E0%B4%99%E0%B5%BE" title="അവസ്ഥാന്തരങ്ങൾ – Malayalam" lang="ml" hreflang="ml" data-title="അവസ്ഥാന്തരങ്ങൾ" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Peralihan_fasa" title="Peralihan fasa – Malay" lang="ms" hreflang="ms" data-title="Peralihan fasa" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D3%A8%D3%A9%D1%80%D1%87%D0%BB%D3%A9%D0%BB%D1%82%D0%B8%D0%B9%D0%BD_%D2%AF%D0%B5_%D1%88%D0%B0%D1%82" title="Өөрчлөлтийн үе шат – Mongolian" lang="mn" hreflang="mn" data-title="Өөрчлөлтийн үе шат" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A1%E1%80%86%E1%80%84%E1%80%B7%E1%80%BA%E1%80%80%E1%80%B0%E1%80%B8%E1%80%95%E1%80%BC%E1%80%B1%E1%80%AC%E1%80%84%E1%80%BA%E1%80%B8%E1%80%81%E1%80%BC%E1%80%84%E1%80%BA%E1%80%B8" title="အဆင့်ကူးပြောင်းခြင်း – Burmese" lang="my" hreflang="my" data-title="အဆင့်ကူးပြောင်းခြင်း" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Faseovergang" title="Faseovergang – Dutch" lang="nl" hreflang="nl" data-title="Faseovergang" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%9B%B8%E8%BB%A2%E7%A7%BB" title="相転移 – Japanese" lang="ja" hreflang="ja" data-title="相転移" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Faseovergang" title="Faseovergang – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Faseovergang" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Faseovergang" title="Faseovergang – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Faseovergang" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Fazaviy_o%CA%BBtish" title="Fazaviy oʻtish – Uzbek" lang="uz" hreflang="uz" data-title="Fazaviy oʻtish" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%AF_%D9%81%D8%A7%D8%B2_%D8%A8%D8%AF%D9%84%D9%88%D9%86" title="د فاز بدلون – Pashto" lang="ps" hreflang="ps" data-title="د فاز بدلون" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Przemiana_fazowa" title="Przemiana fazowa – Polish" lang="pl" hreflang="pl" data-title="Przemiana fazowa" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Transi%C3%A7%C3%A3o_de_fase" title="Transição de fase – Portuguese" lang="pt" hreflang="pt" data-title="Transição de fase" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Transformare_de_faz%C4%83" title="Transformare de fază – Romanian" lang="ro" hreflang="ro" data-title="Transformare de fază" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A4%D0%B0%D0%B7%D0%BE%D0%B2%D1%8B%D0%B9_%D0%BF%D0%B5%D1%80%D0%B5%D1%85%D0%BE%D0%B4" title="Фазовый переход – Russian" lang="ru" hreflang="ru" data-title="Фазовый переход" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Phase_change" title="Phase change – Simple English" lang="en-simple" hreflang="en-simple" data-title="Phase change" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/F%C3%A1zov%C3%A1_premena" title="Fázová premena – Slovak" lang="sk" hreflang="sk" data-title="Fázová premena" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Fazni_prehod" title="Fazni prehod – Slovenian" lang="sl" hreflang="sl" data-title="Fazni prehod" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A4%D0%B0%D0%B7%D0%BD%D0%B0_%D1%82%D1%80%D0%B0%D0%BD%D1%81%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%86%D0%B8%D1%98%D0%B0" title="Фазна трансформација – Serbian" lang="sr" hreflang="sr" data-title="Фазна трансформација" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Fazna_transformacija" title="Fazna transformacija – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Fazna transformacija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Faasimuutos" title="Faasimuutos – Finnish" lang="fi" hreflang="fi" data-title="Faasimuutos" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Fas%C3%B6verg%C3%A5ng" title="Fasövergång – Swedish" lang="sv" hreflang="sv" data-title="Fasövergång" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A8%E0%AE%BF%E0%AE%B2%E0%AF%88_%E0%AE%AE%E0%AE%BE%E0%AE%B1%E0%AF%8D%E0%AE%B1%E0%AE%AE%E0%AF%8D" title="நிலை மாற்றம் – Tamil" lang="ta" hreflang="ta" data-title="நிலை மாற்றம்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/H%C3%A2l_de%C4%9Fi%C5%9Fimi" title="Hâl değişimi – Turkish" lang="tr" hreflang="tr" data-title="Hâl değişimi" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A4%D0%B0%D0%B7%D0%BE%D0%B2%D0%B8%D0%B9_%D0%BF%D0%B5%D1%80%D0%B5%D1%85%D1%96%D0%B4" title="Фазовий перехід – Ukrainian" lang="uk" hreflang="uk" data-title="Фазовий перехід" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Chuy%E1%BB%83n_pha" 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<div id="contentSub"><div id="mw-content-subtitle"><span class="mw-redirectedfrom">(Redirected from <a href="/w/index.php?title=Phase_Transformation&redirect=no" class="mw-redirect" title="Phase Transformation">Phase Transformation</a>)</span></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Physical process of transition between basic states of matter</div> <p class="mw-empty-elt"> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Phase_change_-_en.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Phase_change_-_en.svg/320px-Phase_change_-_en.svg.png" decoding="async" width="320" height="340" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Phase_change_-_en.svg/480px-Phase_change_-_en.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Phase_change_-_en.svg/640px-Phase_change_-_en.svg.png 2x" data-file-width="493" data-file-height="524" /></a><figcaption>This diagram shows the nomenclature for the different phase transitions.</figcaption></figure> <p>In <a href="/wiki/Physics" title="Physics">physics</a>, <a href="/wiki/Chemistry" title="Chemistry">chemistry</a>, and other related fields like biology, a <b>phase transition</b> (or <b>phase change</b>) is the <a href="/wiki/Physical_process" class="mw-redirect" title="Physical process">physical process</a> of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic <a href="/wiki/State_of_matter" title="State of matter">states of matter</a>: <a href="/wiki/Solid" title="Solid">solid</a>, <a href="/wiki/Liquid" title="Liquid">liquid</a>, and <a href="/wiki/Gas" title="Gas">gas</a>, and in rare cases, <a href="/wiki/Plasma_(physics)" title="Plasma (physics)">plasma</a>. A phase of a <a href="/wiki/Thermodynamic_system" title="Thermodynamic system">thermodynamic system</a> and the states of matter have uniform <a href="/wiki/Physical_property" title="Physical property">physical properties</a>. During a phase transition of a given medium, certain properties of the medium change as a result of the change of external conditions, such as <a href="/wiki/Temperature" title="Temperature">temperature</a> or <a href="/wiki/Pressure" title="Pressure">pressure</a>. This can be a discontinuous change; for example, a liquid may become gas upon heating to its <a href="/wiki/Boiling_point" title="Boiling point">boiling point</a>, resulting in an abrupt change in volume. The identification of the external conditions at which a transformation occurs defines the phase transition point. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Types_of_phase_transition">Types of phase transition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Phase_transition&action=edit&section=1" title="Edit section: Types of phase transition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="States_of_matter">States of matter</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Phase_transition&action=edit&section=2" title="Edit section: States of matter"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Phase_diagram_of_water_simplified.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Phase_diagram_of_water_simplified.svg/250px-Phase_diagram_of_water_simplified.svg.png" decoding="async" width="250" height="185" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Phase_diagram_of_water_simplified.svg/375px-Phase_diagram_of_water_simplified.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/33/Phase_diagram_of_water_simplified.svg/500px-Phase_diagram_of_water_simplified.svg.png 2x" data-file-width="512" data-file-height="379" /></a><figcaption>A simplified phase diagram for <a href="/wiki/Water" title="Water">water</a>, showing whether solid ice, liquid water, or gaseous water vapor is the most stable at different combinations of temperature and pressure.</figcaption></figure> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Vapor_pressure" title="Vapor pressure">vapor pressure</a> and <a href="/wiki/Phase_diagram" title="Phase diagram">phase diagram</a></div> <p>Phase transitions commonly refer to when a substance transforms between one of the four <a href="/wiki/State_of_matter" title="State of matter">states of matter</a> to another. At the phase transition point for a substance, for instance the <a href="/wiki/Boiling_point" title="Boiling point">boiling point</a>, the two phases involved - liquid and <a href="/wiki/Vapor" title="Vapor">vapor</a>, have identical free energies and therefore are equally likely to exist. Below the boiling point, the liquid is the more stable state of the two, whereas above the boiling point the gaseous form is the more stable. </p><p>Common transitions between the solid, liquid, and gaseous phases of a single component, due to the effects of temperature and/or <a href="/wiki/Pressure" title="Pressure">pressure</a> are identified in the following table: </p> <table class="wikitable" style="background:transparent; border:none; text-align:center;"> <caption><a class="mw-selflink selflink">Phase transitions</a> of matter (<style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist 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dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Table_of_phase_transitions" title="Template:Table of phase transitions"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Table_of_phase_transitions" title="Template talk:Table of phase transitions"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Table_of_phase_transitions" title="Special:EditPage/Template:Table of phase transitions"><abbr title="Edit this template">e</abbr></a></li></ul></div>) </caption> <tbody><tr> <th style="background:#EAECF0;background:linear-gradient(to top right,#EAECF0 49%,#AAA 49.5%,#AAA 50.5%,#EAECF0 51%);line-height:1.2;padding:0.1em 0.4em;"><div style="margin-left:2em;text-align:right">To</div><div style="margin-right:2em;text-align:left">From</div> </th> <th><a href="/wiki/Solid" title="Solid">Solid</a> </th> <th><a href="/wiki/Liquid" title="Liquid">Liquid</a> </th> <th><a href="/wiki/Gas" title="Gas">Gas</a> </th> <th><a href="/wiki/Plasma_(physics)" title="Plasma (physics)">Plasma</a> </th></tr> <tr> <th>Solid </th> <td style="background:#EAECF0;background:linear-gradient(to top right,#EAECF0 49%,#AAA 49.5%,#AAA 50.5%,#EAECF0 51%);line-height:1.2;padding:0.1em 0.4em;"><div style="margin-left:2em;text-align:right"></div><div style="margin-right:2em;text-align:left"></div> </td> <td><a href="/wiki/Melting" title="Melting">Melting</a> </td> <td><a href="/wiki/Sublimation_(phase_transition)" title="Sublimation (phase transition)">Sublimation</a> </td> <td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na"> </td></tr> <tr> <th>Liquid </th> <td><a href="/wiki/Freezing" title="Freezing">Freezing</a> </td> <td style="background:#EAECF0;background:linear-gradient(to top right,#EAECF0 49%,#AAA 49.5%,#AAA 50.5%,#EAECF0 51%);line-height:1.2;padding:0.1em 0.4em;"><div style="margin-left:2em;text-align:right"></div><div style="margin-right:2em;text-align:left"></div> </td> <td><a href="/wiki/Vaporization" title="Vaporization">Vaporization</a> </td> <td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na"> </td></tr> <tr> <th>Gas </th> <td><a href="/wiki/Deposition_(phase_transition)" title="Deposition (phase transition)">Deposition</a> </td> <td><a href="/wiki/Condensation" title="Condensation">Condensation</a> </td> <td style="background:#EAECF0;background:linear-gradient(to top right,#EAECF0 49%,#AAA 49.5%,#AAA 50.5%,#EAECF0 51%);line-height:1.2;padding:0.1em 0.4em;"><div style="margin-left:2em;text-align:right"></div><div style="margin-right:2em;text-align:left"></div> </td> <td><a href="/wiki/Ionization" title="Ionization">Ionization</a> </td></tr> <tr> <th>Plasma </th> <td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na"> </td> <td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na"> </td> <td><a href="/wiki/Plasma_recombination" title="Plasma recombination">Recombination</a> </td> <td style="background:#EAECF0;background:linear-gradient(to top right,#EAECF0 49%,#AAA 49.5%,#AAA 50.5%,#EAECF0 51%);line-height:1.2;padding:0.1em 0.4em;"><div style="margin-left:2em;text-align:right"></div><div style="margin-right:2em;text-align:left"></div> </td></tr></tbody></table> <p>For a single component, the most stable phase at different temperatures and pressures can be shown on a <a href="/wiki/Phase_diagram" title="Phase diagram">phase diagram</a>. Such a diagram usually depicts states in equilibrium. A phase transition usually occurs when the pressure or temperature changes and the system crosses from one region to another, like water turning from liquid to solid as soon as the temperature drops below the <a href="/wiki/Freezing_point" class="mw-redirect" title="Freezing point">freezing point</a>. In exception to the usual case, it is sometimes possible to change the state of a system <a href="/wiki/Adiabatic" class="mw-redirect" title="Adiabatic">diabatically</a> (as opposed to <a href="/wiki/Adiabatic_invariant" title="Adiabatic invariant">adiabatically</a>) in such a way that it can be brought past a phase transition point without undergoing a phase transition. The resulting state is <a href="/wiki/Metastable" class="mw-redirect" title="Metastable">metastable</a>, i.e., less stable than the phase to which the transition would have occurred, but not unstable either. This occurs in <a href="/wiki/Superheating" title="Superheating">superheating</a> and <a href="/wiki/Supercooling" title="Supercooling">supercooling</a>, for example. Metastable states do not appear on usual phase diagrams. </p> <div class="mw-heading mw-heading3"><h3 id="Structural">Structural</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Phase_transition&action=edit&section=3" title="Edit section: Structural"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Polymorphism_(materials_science)" class="mw-redirect" title="Polymorphism (materials science)">Polymorphism (materials science)</a></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Pure_iron_phase_diagram_(EN).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Pure_iron_phase_diagram_%28EN%29.svg/250px-Pure_iron_phase_diagram_%28EN%29.svg.png" decoding="async" width="250" height="222" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Pure_iron_phase_diagram_%28EN%29.svg/375px-Pure_iron_phase_diagram_%28EN%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Pure_iron_phase_diagram_%28EN%29.svg/500px-Pure_iron_phase_diagram_%28EN%29.svg.png 2x" data-file-width="675" data-file-height="600" /></a><figcaption>A phase diagram showing the <a href="/wiki/Allotropes_of_iron" title="Allotropes of iron">allotropes of iron</a>, distinguishing between several different <a href="/wiki/Crystal_structure" title="Crystal structure">crystal structures</a> including <a href="/wiki/Allotropes_of_iron" title="Allotropes of iron">ferrite</a> (α-iron) and <a href="/wiki/Austenite" title="Austenite">austenite</a> (γ-iron).</figcaption></figure> <p>Phase transitions can also occur when a solid changes to a different structure without changing its chemical makeup. In elements, this is known as <a href="/wiki/Allotropy" title="Allotropy">allotropy</a>, whereas in compounds it is known as <a href="/wiki/Polymorphism_(materials_science)" class="mw-redirect" title="Polymorphism (materials science)">polymorphism</a>. The change from one <a href="/wiki/Crystal_structure" title="Crystal structure">crystal structure</a> to another, from a crystalline solid to an <a href="/wiki/Amorphous_solid" title="Amorphous solid">amorphous solid</a>, or from one amorphous structure to another (<a href="/wiki/Polyamorphism" title="Polyamorphism">polyamorphs</a>) are all examples of solid to solid phase transitions. </p><p>The <a href="/wiki/Martensitic_transformation" class="mw-redirect" title="Martensitic transformation">martensitic transformation</a> occurs as one of the many phase transformations in carbon steel and stands as a model for <a href="/wiki/Displacive_phase_transformations" class="mw-redirect" title="Displacive phase transformations">displacive phase transformations</a>. Order-disorder transitions such as in alpha-<a href="/wiki/Titanium_aluminide" title="Titanium aluminide">titanium aluminides</a>. As with states of matter, there is also a <a href="/wiki/Metastable" class="mw-redirect" title="Metastable">metastable</a> to equilibrium phase transformation for structural phase transitions. A metastable polymorph which forms rapidly due to lower surface energy will transform to an equilibrium phase given sufficient thermal input to overcome an energetic barrier. </p> <div class="mw-heading mw-heading3"><h3 id="Magnetic">Magnetic</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Phase_transition&action=edit&section=4" title="Edit section: Magnetic"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Magnetic_structure" title="Magnetic structure">Magnetic structure</a></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:MnSi_magnetic_phase_diagram.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c6/MnSi_magnetic_phase_diagram.png/250px-MnSi_magnetic_phase_diagram.png" decoding="async" width="250" height="223" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c6/MnSi_magnetic_phase_diagram.png/375px-MnSi_magnetic_phase_diagram.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c6/MnSi_magnetic_phase_diagram.png/500px-MnSi_magnetic_phase_diagram.png 2x" data-file-width="609" data-file-height="543" /></a><figcaption>A phase diagram showing different <a href="/wiki/Magnetic_structure" title="Magnetic structure">magnetic structures</a> in the same crystal structure of <a href="/wiki/Manganese_monosilicide" title="Manganese monosilicide">Manganese monosilicide</a>.</figcaption></figure> <p>Phase transitions can also describe the change between different kinds of <a href="/wiki/Magnetic_ordering" class="mw-redirect" title="Magnetic ordering">magnetic ordering</a>. The most well-known is the transition between the <a href="/wiki/Ferromagnetism" title="Ferromagnetism">ferromagnetic</a> and <a href="/wiki/Paramagnetism" title="Paramagnetism">paramagnetic</a> phases of <a href="/wiki/Magnet" title="Magnet">magnetic</a> materials, which occurs at what is called the <a href="/wiki/Curie_point" class="mw-redirect" title="Curie point">Curie point</a>. Another example is the transition between differently ordered, <a href="/wiki/ANNNI_model" title="ANNNI model">commensurate</a> or <a href="/wiki/Commensurability_(mathematics)" title="Commensurability (mathematics)">incommensurate</a>, magnetic structures, such as in cerium <a href="/wiki/Antimonide" title="Antimonide">antimonide</a>. A simplified but highly useful model of magnetic phase transitions is provided by the <a href="/wiki/Ising_Model" class="mw-redirect" title="Ising Model">Ising Model</a> </p> <div class="mw-heading mw-heading3"><h3 id="Mixtures">Mixtures</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Phase_transition&action=edit&section=5" title="Edit section: Mixtures"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Binary_phase_diagram_of_NiTI_(phase_and_temperature).JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Binary_phase_diagram_of_NiTI_%28phase_and_temperature%29.JPG/250px-Binary_phase_diagram_of_NiTI_%28phase_and_temperature%29.JPG" decoding="async" width="250" height="206" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Binary_phase_diagram_of_NiTI_%28phase_and_temperature%29.JPG/375px-Binary_phase_diagram_of_NiTI_%28phase_and_temperature%29.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Binary_phase_diagram_of_NiTI_%28phase_and_temperature%29.JPG/500px-Binary_phase_diagram_of_NiTI_%28phase_and_temperature%29.JPG 2x" data-file-width="929" data-file-height="764" /></a><figcaption>A binary phase diagram showing the most stable chemical compounds of <a href="/wiki/Titanium" title="Titanium">titanium</a> and <a href="/wiki/Nickel" title="Nickel">nickel</a> at different <a href="/wiki/Mixing_ratio" title="Mixing ratio">mixing ratios</a> and <a href="/wiki/Temperature" title="Temperature">temperatures</a>.</figcaption></figure> <p>Phase transitions involving <a href="/wiki/Solution_(chemistry)" title="Solution (chemistry)">solutions</a> and <a href="/wiki/Mixture" title="Mixture">mixtures</a> are more complicated than transitions involving a single compound. While chemically pure compounds exhibit a single temperature <a href="/wiki/Melting_point" title="Melting point">melting point</a> between solid and liquid phases, mixtures can either have a single melting point, known as <a href="/wiki/Congruent_melting" title="Congruent melting">congruent melting</a>, or they have different <a href="/wiki/Liquidus_and_solidus" title="Liquidus and solidus">liquidus and solidus temperatures</a> resulting in a temperature span where solid and liquid coexist in equilibrium. This is often the case in <a href="/wiki/Solid_solution" title="Solid solution">solid solutions</a>, where the two components are isostructural. </p><p>There are also a number of phase transitions involving three phases: a <a href="/wiki/Eutectic" class="mw-redirect" title="Eutectic">eutectic</a> transformation, in which a two-component single-phase liquid is cooled and transforms into two solid phases. The same process, but beginning with a solid instead of a liquid is called a <a href="/wiki/Eutectoid" class="mw-redirect" title="Eutectoid">eutectoid</a> transformation. A <a href="/wiki/Peritectic" class="mw-redirect" title="Peritectic">peritectic</a> transformation, in which a two-component single-phase solid is heated and transforms into a solid phase and a liquid phase. A <a href="/wiki/Peritectoid" class="mw-redirect" title="Peritectoid">peritectoid</a> reaction is a peritectoid reaction, except involving only solid phases. A <a href="/w/index.php?title=Monotectic&action=edit&redlink=1" class="new" title="Monotectic (page does not exist)">monotectic</a> reaction consists of change from a liquid and to a combination of a solid and a second liquid, where the two liquids display a <a href="/wiki/Miscibility_gap" title="Miscibility gap">miscibility gap</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Separation into multiple phases can occur via <a href="/wiki/Spinodal_decomposition" title="Spinodal decomposition">spinodal decomposition</a>, in which a single phase is cooled and separates into two different compositions. </p><p>Non-equilibrium mixtures can occur, such as in <a href="/wiki/Supersaturation" title="Supersaturation">supersaturation</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Other_examples">Other examples</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Phase_transition&action=edit&section=6" title="Edit section: Other examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Argon_ice_1.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Argon_ice_1.jpg/220px-Argon_ice_1.jpg" decoding="async" width="220" height="196" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Argon_ice_1.jpg/330px-Argon_ice_1.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Argon_ice_1.jpg/440px-Argon_ice_1.jpg 2x" data-file-width="1829" data-file-height="1632" /></a><figcaption>A small piece of rapidly melting solid <a href="/wiki/Argon" title="Argon">argon</a> shows two concurrent phase changes. The transition from solid to liquid, and gas to liquid (shown by the white condensed water vapour).</figcaption></figure> <p>Other phase changes include: </p> <ul><li>Transition to a <a href="/wiki/Mesophase" title="Mesophase">mesophase</a> between solid and liquid, such as one of the "<a href="/wiki/Liquid_crystal" title="Liquid crystal">liquid crystal</a>" phases.</li> <li>The dependence of the <a href="/wiki/Adsorption" title="Adsorption">adsorption</a> geometry on coverage and temperature, such as for <a href="/wiki/Hydrogen" title="Hydrogen">hydrogen</a> on iron (110).</li> <li>The emergence of <a href="/wiki/Superconductivity" title="Superconductivity">superconductivity</a> in certain metals and ceramics when cooled below a critical temperature.</li> <li>The emergence of <a href="/wiki/Metamaterial" title="Metamaterial">metamaterial</a> properties in artificial photonic media as their parameters are varied.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup></li> <li>Quantum condensation of <a href="/wiki/Boson" title="Boson">bosonic</a> fluids (<a href="/wiki/Bose%E2%80%93Einstein_condensate" title="Bose–Einstein condensate">Bose–Einstein condensation</a>). The <a href="/wiki/Superfluidity" title="Superfluidity">superfluid</a> transition in liquid <a href="/wiki/Helium" title="Helium">helium</a> is an example of this.</li> <li>The <a href="/wiki/Symmetry_breaking" title="Symmetry breaking">breaking of symmetries</a> in the laws of physics during the early history of the universe as its temperature cooled.</li> <li><a href="/wiki/Isotope_fractionation" title="Isotope fractionation">Isotope fractionation</a> occurs during a phase transition, the ratio of light to heavy isotopes in the involved molecules changes. When <a href="/wiki/Water_vapor" title="Water vapor">water vapor</a> condenses (an <a href="/wiki/Equilibrium_fractionation" title="Equilibrium fractionation">equilibrium fractionation</a>), the heavier water isotopes (<sup>18</sup>O and <sup>2</sup>H) become enriched in the liquid phase while the lighter isotopes (<sup>16</sup>O and <sup>1</sup>H) tend toward the vapor phase.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></li></ul> <p>Phase transitions occur when the <a href="/wiki/Thermodynamic_free_energy" title="Thermodynamic free energy">thermodynamic free energy</a> of a system is <a href="/wiki/Analytic_function" title="Analytic function">non-analytic</a> for some choice of thermodynamic variables (cf. <a href="/wiki/Phase_(matter)" title="Phase (matter)">phases</a>). This condition generally stems from the interactions of a large number of particles in a system, and does not appear in systems that are small. Phase transitions can occur for non-thermodynamic systems, where temperature is not a parameter. Examples include: <a href="/wiki/Quantum_phase_transition" title="Quantum phase transition">quantum phase transitions</a>, dynamic phase transitions, and topological (structural) phase transitions. In these types of systems other parameters take the place of temperature. 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nomobile nowraplinks hlist"><tbody><tr><th class="sidebar-title"><a href="/wiki/Condensed_matter_physics" title="Condensed matter physics">Condensed matter physics</a></th></tr><tr><td class="sidebar-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:QuantumPhaseTransition.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/QuantumPhaseTransition.svg/220px-QuantumPhaseTransition.svg.png" decoding="async" width="220" height="159" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/QuantumPhaseTransition.svg/330px-QuantumPhaseTransition.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/10/QuantumPhaseTransition.svg/440px-QuantumPhaseTransition.svg.png 2x" data-file-width="512" data-file-height="369" /></a></span></td></tr><tr><td class="sidebar-content"> <div class="hlist"><ul><li><a href="/wiki/Phase_(matter)" title="Phase (matter)">Phases</a></li><li><a class="mw-selflink selflink">Phase transition</a></li><li><a href="/wiki/Quantum_critical_point" title="Quantum critical point">QCP</a></li></ul></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/State_of_matter" title="State of matter">States of matter</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"><ul><li><a href="/wiki/Solid" title="Solid">Solid</a></li><li><a href="/wiki/Liquid" title="Liquid">Liquid</a></li><li><a href="/wiki/Gas" title="Gas">Gas</a></li><li><a href="/wiki/Plasma_(physics)" title="Plasma (physics)">Plasma</a></li><li><a href="/wiki/Bose%E2%80%93Einstein_condensate" title="Bose–Einstein condensate">Bose–Einstein condensate</a></li><li><a href="/wiki/Bose_gas" title="Bose gas">Bose gas</a></li><li><a href="/wiki/Fermionic_condensate" title="Fermionic condensate">Fermionic condensate</a></li><li><a href="/wiki/Fermi_gas" title="Fermi gas">Fermi gas</a></li><li><a href="/wiki/Fermi_liquid_theory" title="Fermi liquid theory">Fermi liquid</a></li><li><a href="/wiki/Supersolid" title="Supersolid">Supersolid</a></li><li><a href="/wiki/Superfluidity" title="Superfluidity">Superfluidity</a></li><li><a href="/wiki/Luttinger_liquid" title="Luttinger liquid">Luttinger liquid</a></li><li><a href="/wiki/Time_crystal" title="Time crystal">Time crystal</a></li></ul></div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Phase phenomena</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"><ul><li><a href="/wiki/Order_parameter" class="mw-redirect" title="Order parameter">Order parameter</a></li><li><a class="mw-selflink selflink">Phase transition</a></li><li><a href="/wiki/Quantum_critical_point" title="Quantum critical point">QCP</a></li></ul></div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Electronic phases</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"><ul><li><a href="/wiki/Electronic_band_structure" title="Electronic band structure">Electronic band structure</a></li><li><a href="/wiki/Plasma_(physics)" title="Plasma (physics)">Plasma</a></li><li><a href="/wiki/Insulator_(electricity)" title="Insulator (electricity)">Insulator</a></li><li><a href="/wiki/Mott_insulator" title="Mott insulator">Mott insulator</a></li><li><a href="/wiki/Semiconductor" title="Semiconductor">Semiconductor</a></li><li><a href="/wiki/Semimetal" title="Semimetal">Semimetal</a></li><li><a href="/wiki/Electrical_conductor" title="Electrical conductor">Conductor</a></li><li><a href="/wiki/Superconductivity" title="Superconductivity">Superconductor</a></li><li><a href="/wiki/Thermoelectric_effect" title="Thermoelectric effect">Thermoelectric</a></li><li><a href="/wiki/Piezoelectricity" title="Piezoelectricity">Piezoelectric</a></li><li><a href="/wiki/Ferroelectricity" title="Ferroelectricity">Ferroelectric</a></li><li><a href="/wiki/Topological_insulator" title="Topological insulator">Topological insulator</a></li><li><a href="/wiki/Spin_gapless_semiconductor" title="Spin gapless semiconductor">Spin gapless semiconductor</a></li></ul></div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Electronic phenomena</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"><ul><li><a href="/wiki/Quantum_Hall_effect" title="Quantum Hall effect">Quantum Hall effect</a></li><li><a href="/wiki/Spin_Hall_effect" title="Spin Hall effect">Spin Hall effect</a></li><li><a href="/wiki/Kondo_effect" title="Kondo effect">Kondo effect</a></li></ul></div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Magnetic phases</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"><ul><li><a href="/wiki/Diamagnetism" title="Diamagnetism">Diamagnet</a></li><li><a href="/wiki/Superdiamagnetism" title="Superdiamagnetism">Superdiamagnet</a><br /> <a href="/wiki/Paramagnetism" title="Paramagnetism">Paramagnet</a></li><li><a href="/wiki/Superparamagnetism" title="Superparamagnetism">Superparamagnet</a><br /><a href="/wiki/Ferromagnetism" title="Ferromagnetism">Ferromagnet</a></li><li><a href="/wiki/Antiferromagnetism" title="Antiferromagnetism">Antiferromagnet</a><br /><a href="/wiki/Metamagnetism" title="Metamagnetism">Metamagnet</a></li><li><a href="/wiki/Spin_glass" title="Spin glass">Spin glass</a></li></ul></div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Quasiparticle" title="Quasiparticle">Quasiparticles</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"><ul><li><a href="/wiki/Phonon" title="Phonon">Phonon</a></li><li><a href="/wiki/Exciton" title="Exciton">Exciton</a></li><li><a href="/wiki/Plasmon" title="Plasmon">Plasmon</a><br /><a href="/wiki/Polariton" title="Polariton">Polariton</a></li><li><a href="/wiki/Polaron" title="Polaron">Polaron</a></li><li><a href="/wiki/Magnon" title="Magnon">Magnon</a></li><li><a href="/wiki/Roton" title="Roton">Roton</a></li></ul></div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Soft_matter" title="Soft matter">Soft matter</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"><ul><li><a href="/wiki/Amorphous_solid" title="Amorphous solid">Amorphous solid</a></li><li><a href="/wiki/Colloid" title="Colloid">Colloid</a></li><li><a href="/wiki/Granular_material" title="Granular material">Granular material</a></li><li><a href="/wiki/Liquid_crystal" title="Liquid crystal">Liquid crystal</a></li><li><a href="/wiki/Polymer" title="Polymer">Polymer</a></li></ul></div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Scientists</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"><ul><li><a href="/wiki/Johannes_Diderik_van_der_Waals" title="Johannes Diderik van der Waals">Van der Waals</a></li><li><a href="/wiki/Heike_Kamerlingh_Onnes" title="Heike Kamerlingh Onnes">Onnes</a></li><li><a href="/wiki/Max_von_Laue" title="Max von Laue">von Laue</a></li><li><a href="/wiki/William_Henry_Bragg" title="William Henry Bragg">Bragg</a></li><li><a href="/wiki/Peter_Debye" title="Peter Debye">Debye</a></li><li><a href="/wiki/Felix_Bloch" title="Felix Bloch">Bloch</a></li><li><a href="/wiki/Lars_Onsager" title="Lars Onsager">Onsager</a></li><li><a href="/wiki/Neville_Mott" class="mw-redirect" title="Neville Mott">Mott</a></li><li><a href="/wiki/Rudolf_Peierls" title="Rudolf Peierls">Peierls</a></li><li><a href="/wiki/Lev_Landau" title="Lev Landau">Landau</a></li><li><a href="/wiki/Luttinger" class="mw-redirect" title="Luttinger">Luttinger</a></li><li><a href="/wiki/Philip_Warren_Anderson" class="mw-redirect" title="Philip Warren Anderson">Anderson</a></li><li><a href="/wiki/John_Hasbrouck_Van_Vleck" title="John Hasbrouck Van Vleck">Van Vleck</a></li><li><a href="/wiki/John_Hubbard_(physicist)" title="John Hubbard (physicist)">Hubbard</a></li><li><a href="/wiki/William_Bradford_Shockley" class="mw-redirect" title="William Bradford Shockley">Shockley</a></li><li><a href="/wiki/John_Bardeen" title="John Bardeen">Bardeen</a></li><li><a href="/wiki/Leon_Cooper" title="Leon Cooper">Cooper</a></li><li><a href="/wiki/John_Robert_Schrieffer" title="John Robert Schrieffer">Schrieffer</a></li><li><a href="/wiki/Brian_Josephson" title="Brian Josephson">Josephson</a></li><li><a href="/wiki/Louis_N%C3%A9el" title="Louis Néel">Louis Néel</a></li><li><a href="/wiki/Leo_Esaki" title="Leo Esaki">Esaki</a></li><li><a href="/wiki/Ivar_Giaever" title="Ivar Giaever">Giaever</a></li><li><a href="/wiki/Walter_Kohn" title="Walter Kohn">Kohn</a></li><li><a href="/wiki/Leo_Kadanoff" title="Leo Kadanoff">Kadanoff</a></li><li><a href="/wiki/Michael_Fisher" title="Michael Fisher">Fisher</a></li><li><a href="/wiki/Kenneth_G._Wilson" title="Kenneth G. Wilson">Wilson</a></li><li><a href="/wiki/Klaus_von_Klitzing" title="Klaus von Klitzing">von Klitzing</a></li><li><a href="/wiki/Gerd_Binnig" title="Gerd Binnig">Binnig</a></li><li><a href="/wiki/Heinrich_Rohrer" title="Heinrich Rohrer">Rohrer</a></li><li><a href="/wiki/Johannes_Georg_Bednorz" class="mw-redirect" title="Johannes Georg Bednorz">Bednorz</a></li><li><a href="/wiki/Karl_Alexander_M%C3%BCller" class="mw-redirect" title="Karl Alexander Müller">Müller</a></li><li><a href="/wiki/Robert_B._Laughlin" title="Robert B. Laughlin">Laughlin</a></li><li><a href="/wiki/Horst_Ludwig_St%C3%B6rmer" title="Horst Ludwig Störmer">Störmer</a></li><li><a href="/wiki/Yang_Chen-Ning" title="Yang Chen-Ning">Yang</a></li><li><a href="/wiki/Daniel_C._Tsui" title="Daniel C. Tsui">Tsui</a></li><li><a href="/wiki/Alexei_Alexeyevich_Abrikosov" class="mw-redirect" title="Alexei Alexeyevich Abrikosov">Abrikosov</a></li><li><a href="/wiki/Vitaly_Lazarevich_Ginzburg" class="mw-redirect" title="Vitaly Lazarevich Ginzburg">Ginzburg</a></li><li><a href="/wiki/Anthony_James_Leggett" title="Anthony James Leggett">Leggett</a></li><li><a href="/wiki/Giorgio_Parisi" title="Giorgio Parisi">Parisi</a></li><li><a href="/wiki/Christof_Wetterich" title="Christof Wetterich">Wetterich</a></li><li><a href="/wiki/John_Perdew" title="John Perdew">Perdew</a></li></ul></div></div></div></td> </tr><tr><td class="sidebar-below hlist" style="background-color: transparent; border-color: #A2B8BF"> <ul><li><span class="nowrap"><span class="nowrap"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/14px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png" decoding="async" width="14" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/21px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/28px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 2x" data-file-width="530" data-file-height="600" /></a></span> </span><a href="/wiki/Portal:Physics" title="Portal:Physics">Physics portal</a></span></li> <li><span class="nowrap"><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Condensed_matter_physics" title="Category:Condensed matter physics">Category</a></span></li></ul></td></tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Condensed_matter_physics" title="Template:Condensed matter physics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Condensed_matter_physics" title="Template talk:Condensed matter physics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Condensed_matter_physics" title="Special:EditPage/Template:Condensed matter physics"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Classifications">Classifications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Phase_transition&action=edit&section=7" title="Edit section: Classifications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Ehrenfest_classification">Ehrenfest classification</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Phase_transition&action=edit&section=8" title="Edit section: Ehrenfest classification"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Paul_Ehrenfest" title="Paul Ehrenfest">Paul Ehrenfest</a> classified phase transitions based on the behavior of the <a href="/wiki/Thermodynamic_free_energy" title="Thermodynamic free energy">thermodynamic free energy</a> as a function of other thermodynamic variables.<sup id="cite_ref-ReferenceA_5-0" class="reference"><a href="#cite_note-ReferenceA-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Under this scheme, phase transitions were labeled by the lowest derivative of the free energy that is discontinuous at the transition. <i>First-order phase transitions</i> exhibit a discontinuity in the first derivative of the free energy with respect to some thermodynamic variable.<sup id="cite_ref-Blundell_6-0" class="reference"><a href="#cite_note-Blundell-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> The various solid/liquid/gas transitions are classified as first-order transitions because they involve a discontinuous change in density, which is the (inverse of the) first derivative of the free energy with respect to pressure. <i>Second-order phase transitions</i> are continuous in the first derivative (the <a href="#order_parameters">order parameter</a>, which is the first derivative of the free energy with respect to the external field, is continuous across the transition) but exhibit discontinuity in a second derivative of the free energy.<sup id="cite_ref-Blundell_6-1" class="reference"><a href="#cite_note-Blundell-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> These include the ferromagnetic phase transition in materials such as iron, where the <a href="/wiki/Magnetization" title="Magnetization">magnetization</a>, which is the first derivative of the free energy with respect to the applied magnetic field strength, increases continuously from zero as the temperature is lowered below the <a href="/wiki/Curie_temperature" title="Curie temperature">Curie temperature</a>. The <a href="/wiki/Magnetic_susceptibility" title="Magnetic susceptibility">magnetic susceptibility</a>, the second derivative of the free energy with the field, changes discontinuously. Under the Ehrenfest classification scheme, there could in principle be third, fourth, and higher-order phase transitions. For example, the Gross–Witten–Wadia phase transition in 2-d lattice quantum chromodynamics is a third-order phase transition.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> The Curie points of many ferromagnetics is also a third-order transition, as shown by their specific heat having a sudden change in slope.<sup id="cite_ref-:0_9-0" class="reference"><a href="#cite_note-:0-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>In practice, only the first- and second-order phase transitions are typically observed. The second-order phase transition was for a while controversial, as it seems to require two sheets of the Gibbs free energy to osculate exactly, which is so unlikely as to never occur in practice. <a href="/wiki/Cornelis_Jacobus_Gorter" title="Cornelis Jacobus Gorter">Cornelis Gorter</a> replied the criticism by pointing out that the Gibbs free energy surface might have two sheets on one side, but only one sheet on the other side, creating a forked appearance.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> (<sup id="cite_ref-:0_9-1" class="reference"><a href="#cite_note-:0-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> pp. 146--150) </p><p>The Ehrenfest classification implicitly allows for continuous phase transformations, where the bonding character of a material changes, but there is no discontinuity in any free energy derivative. An example of this occurs at the <a href="/wiki/Supercritical_liquid%E2%80%93gas_boundaries" title="Supercritical liquid–gas boundaries">supercritical liquid–gas boundaries</a>. </p><p>The first example of a phase transition which did not fit into the Ehrenfest classification was the exact solution of the <a href="/wiki/Ising_model" title="Ising model">Ising model</a>, discovered in 1944 by <a href="/wiki/Lars_Onsager" title="Lars Onsager">Lars Onsager</a>. The exact specific heat differed from the earlier <a href="/wiki/Mean-field_theory" title="Mean-field theory">mean-field</a> approximations, which had predicted that it has a simple discontinuity at critical temperature. Instead, the exact specific heat had a logarithmic divergence at the critical temperature.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> In the following decades, the Ehrenfest classification was replaced by a simplified classification scheme that is able to incorporate such transitions. </p> <div class="mw-heading mw-heading3"><h3 id="Modern_classifications">Modern classifications</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Phase_transition&action=edit&section=9" title="Edit section: Modern classifications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the modern classification scheme, phase transitions are divided into two broad categories, named similarly to the Ehrenfest classes:<sup id="cite_ref-ReferenceA_5-1" class="reference"><a href="#cite_note-ReferenceA-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p><b>First-order phase transitions</b> are those that involve a <a href="/wiki/Latent_heat" title="Latent heat">latent heat</a>. During such a transition, a system either absorbs or releases a fixed (and typically large) amount of energy per volume. During this process, the temperature of the system will stay constant as heat is added: the system is in a "mixed-phase regime" in which some parts of the system have completed the transition and others have not.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p><p>Familiar examples are the melting of ice or the boiling of water (the water does not instantly turn into <a href="/wiki/Water_vapor" title="Water vapor">vapor</a>, but forms a <a href="/wiki/Turbulence" title="Turbulence">turbulent</a> mixture of liquid water and vapor bubbles). <a href="/wiki/Yoseph_Imry" title="Yoseph Imry">Yoseph Imry</a> and Michael Wortis showed that <a href="/wiki/Quenched_disorder" class="mw-redirect" title="Quenched disorder">quenched disorder</a> can broaden a first-order transition. That is, the transformation is completed over a finite range of temperatures, but phenomena like supercooling and superheating survive and hysteresis is observed on thermal cycling.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-KumarPramanik2006_16-0" class="reference"><a href="#cite_note-KumarPramanik2006-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-PasquiniDaroca2008_17-0" class="reference"><a href="#cite_note-PasquiniDaroca2008-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p><p><b><style data-mw-deduplicate="TemplateStyles:r1238216509">.mw-parser-output .vanchor>:target~.vanchor-text{background-color:#b1d2ff}@media screen{html.skin-theme-clientpref-night .mw-parser-output .vanchor>:target~.vanchor-text{background-color:#0f4dc9}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .vanchor>:target~.vanchor-text{background-color:#0f4dc9}}</style><span class="vanchor"><span id="Second-order_phase_transition"></span><span class="vanchor-text">Second-order phase transition</span></span>s</b> are also called <i>"continuous phase transitions"</i>. They are characterized by a divergent susceptibility, an infinite <a href="/wiki/Correlation_function_(statistical_mechanics)" title="Correlation function (statistical mechanics)">correlation length</a>, and a <a href="/wiki/Power_law" title="Power law">power law</a> decay of correlations near <a href="/wiki/Critical_point_(thermodynamics)" title="Critical point (thermodynamics)">criticality</a>. Examples of second-order phase transitions are the <a href="/wiki/Ferromagnetism" title="Ferromagnetism">ferromagnetic</a> transition, superconducting transition (for a <a href="/wiki/Type-I_superconductor" title="Type-I superconductor">Type-I superconductor</a> the phase transition is second-order at zero external field and for a <a href="/wiki/Type-II_superconductor" title="Type-II superconductor">Type-II superconductor</a> the phase transition is second-order for both normal-state–mixed-state and mixed-state–superconducting-state transitions) and the <a href="/wiki/Superfluid" class="mw-redirect" title="Superfluid">superfluid</a> transition. In contrast to viscosity, thermal expansion and heat capacity of amorphous materials show a relatively sudden change at the glass transition temperature<sup id="cite_ref-J._Non-Cryst_2013_18-0" class="reference"><a href="#cite_note-J._Non-Cryst_2013-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> which enables accurate detection using <a href="/wiki/Differential_scanning_calorimetry" title="Differential scanning calorimetry">differential scanning calorimetry</a> measurements. <a href="/wiki/Lev_Landau" title="Lev Landau">Lev Landau</a> gave a <a href="/wiki/Phenomenology_(particle_physics)" class="mw-redirect" title="Phenomenology (particle physics)">phenomenological</a> <a href="/wiki/Landau_theory" title="Landau theory">theory</a> of second-order phase transitions. </p><p>Apart from isolated, simple phase transitions, there exist transition lines as well as <a href="/wiki/Multicritical_point" title="Multicritical point">multicritical points</a>, when varying external parameters like the magnetic field or composition. </p><p>Several transitions are known as <i>infinite-order phase transitions</i>. They are continuous but break no <a href="#Symmetry">symmetries</a>. The most famous example is the <a href="/wiki/Kosterlitz%E2%80%93Thouless_transition" class="mw-redirect" title="Kosterlitz–Thouless transition">Kosterlitz–Thouless transition</a> in the two-dimensional <a href="/wiki/XY_model" class="mw-redirect" title="XY model">XY model</a>. Many <a href="/wiki/Quantum_phase_transition" title="Quantum phase transition">quantum phase transitions</a>, e.g., in <a href="/wiki/Two-dimensional_electron_gas" title="Two-dimensional electron gas">two-dimensional electron gases</a>, belong to this class. </p><p>The <a href="/wiki/Glass_transition" title="Glass transition">liquid–glass transition</a> is observed in many <a href="/wiki/Polymers" class="mw-redirect" title="Polymers">polymers</a> and other liquids that can be <a href="/wiki/Supercooling" title="Supercooling">supercooled</a> far below the melting point of the crystalline phase. This is atypical in several respects. It is not a transition between thermodynamic ground states: it is widely believed that the true ground state is always crystalline. Glass is a <i><a href="/wiki/Quenched_disorder" class="mw-redirect" title="Quenched disorder">quenched disorder</a></i> state, and its entropy, density, and so on, depend on the thermal history. Therefore, the glass transition is primarily a dynamic phenomenon: on cooling a liquid, internal degrees of freedom successively fall out of equilibrium. Some theoretical methods predict an underlying phase transition in the hypothetical limit of infinitely long relaxation times.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> No direct experimental evidence supports the existence of these transitions. </p> <div class="mw-heading mw-heading2"><h2 id="Characteristic_properties">Characteristic properties</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Phase_transition&action=edit&section=10" title="Edit section: Characteristic properties"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Phase_coexistence">Phase coexistence</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Phase_transition&action=edit&section=11" title="Edit section: Phase coexistence"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A disorder-broadened first-order transition occurs over a finite range of temperatures where the fraction of the low-temperature equilibrium phase grows from zero to one (100%) as the temperature is lowered. This continuous variation of the coexisting fractions with temperature raised interesting possibilities. On cooling, some liquids vitrify into a glass rather than transform to the equilibrium crystal phase. This happens if the cooling rate is faster than a critical cooling rate, and is attributed to the molecular motions becoming so slow that the molecules cannot rearrange into the crystal positions.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> This slowing down happens below a glass-formation temperature <i>T</i><sub>g</sub>, which may depend on the applied pressure.<sup id="cite_ref-J._Non-Cryst_2013_18-1" class="reference"><a href="#cite_note-J._Non-Cryst_2013-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> If the first-order freezing transition occurs over a range of temperatures, and <i>T</i><sub>g</sub> falls within this range, then there is an interesting possibility that the transition is arrested when it is partial and incomplete. Extending these ideas to first-order magnetic transitions being arrested at low temperatures, resulted in the observation of incomplete magnetic transitions, with two magnetic phases coexisting, down to the lowest temperature. First reported in the case of a ferromagnetic to anti-ferromagnetic transition,<sup id="cite_ref-ManekarChaudhary2001_23-0" class="reference"><a href="#cite_note-ManekarChaudhary2001-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> such persistent phase coexistence has now been reported across a variety of first-order magnetic transitions. These include colossal-magnetoresistance manganite materials,<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> magnetocaloric materials,<sup id="cite_ref-RoyChattopadhyay2006_26-0" class="reference"><a href="#cite_note-RoyChattopadhyay2006-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> magnetic shape memory materials,<sup id="cite_ref-LakhaniBanerjee2012_27-0" class="reference"><a href="#cite_note-LakhaniBanerjee2012-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> and other materials.<sup id="cite_ref-KushwahaLakhani2009_28-0" class="reference"><a href="#cite_note-KushwahaLakhani2009-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> The interesting feature of these observations of <i>T</i><sub>g</sub> falling within the temperature range over which the transition occurs is that the first-order magnetic transition is influenced by magnetic field, just like the structural transition is influenced by pressure. The relative ease with which magnetic fields can be controlled, in contrast to pressure, raises the possibility that one can study the interplay between <i>T</i><sub>g</sub> and <i>T</i><sub>c</sub> in an exhaustive way. Phase coexistence across first-order magnetic transitions will then enable the resolution of outstanding issues in understanding glasses. </p> <div class="mw-heading mw-heading3"><h3 id="Critical_points">Critical points</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Phase_transition&action=edit&section=12" title="Edit section: Critical points"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In any system containing liquid and gaseous phases, there exists a special combination of pressure and temperature, known as the <a href="/wiki/Critical_point_(thermodynamics)" title="Critical point (thermodynamics)">critical point</a>, at which the transition between liquid and gas becomes a second-order transition. Near the critical point, the fluid is sufficiently hot and compressed that the distinction between the liquid and gaseous phases is almost non-existent. This is associated with the phenomenon of <a href="/wiki/Critical_opalescence" title="Critical opalescence">critical opalescence</a>, a milky appearance of the liquid due to density fluctuations at all possible wavelengths (including those of visible light). </p> <div class="mw-heading mw-heading3"><h3 id="Symmetry">Symmetry</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Phase_transition&action=edit&section=13" title="Edit section: Symmetry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Phase transitions often involve a <a href="/wiki/Symmetry_breaking" title="Symmetry breaking">symmetry breaking</a> process. For instance, the cooling of a fluid into a <a href="/wiki/Crystalline_solid" class="mw-redirect" title="Crystalline solid">crystalline solid</a> breaks continuous <a href="/wiki/Translation_symmetry" class="mw-redirect" title="Translation symmetry">translation symmetry</a>: each point in the fluid has the same properties, but each point in a crystal does not have the same properties (unless the points are chosen from the lattice points of the crystal lattice). Typically, the high-temperature phase contains more symmetries than the low-temperature phase due to <a href="/wiki/Spontaneous_symmetry_breaking" title="Spontaneous symmetry breaking">spontaneous symmetry breaking</a>, with the exception of certain <a href="/wiki/Accidental_symmetry" title="Accidental symmetry">accidental symmetries</a> (e.g. the formation of heavy <a href="/wiki/Virtual_particles" class="mw-redirect" title="Virtual particles">virtual particles</a>, which only occurs at low temperatures).<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Order_parameters">Order parameters</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Phase_transition&action=edit&section=14" title="Edit section: Order parameters"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An <b>order parameter</b> is a measure of the degree of order across the boundaries in a phase transition system; it normally ranges between zero in one phase (usually above the critical point) and nonzero in the other.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> At the critical point, the order parameter <a href="/wiki/Susceptibility_(disambiguation)" class="mw-redirect mw-disambig" title="Susceptibility (disambiguation)">susceptibility</a> will usually diverge. </p><p>An example of an order parameter is the net <a href="/wiki/Magnetization" title="Magnetization">magnetization</a> in a <a href="/wiki/Ferromagnetic" class="mw-redirect" title="Ferromagnetic">ferromagnetic</a> system undergoing a phase transition. For liquid/gas transitions, the order parameter is the difference of the densities. </p><p>From a theoretical perspective, order parameters arise from symmetry breaking. When this happens, one needs to introduce one or more extra variables to describe the state of the system. For example, in the <a href="/wiki/Ferromagnetic" class="mw-redirect" title="Ferromagnetic">ferromagnetic</a> phase, one must provide the net <a href="/wiki/Magnetization" title="Magnetization">magnetization</a>, whose direction was spontaneously chosen when the system cooled below the <a href="/wiki/Curie_point" class="mw-redirect" title="Curie point">Curie point</a>. However, note that order parameters can also be defined for non-symmetry-breaking transitions.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (December 2023)">citation needed</span></a></i>]</sup> </p><p>Some phase transitions, such as <a href="/wiki/Superconductivity" title="Superconductivity">superconducting</a> and ferromagnetic, can have order parameters for more than one degree of freedom. In such phases, the order parameter may take the form of a complex number, a vector, or even a tensor, the magnitude of which goes to zero at the phase transition.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (August 2022)">citation needed</span></a></i>]</sup> </p><p>There also exist dual descriptions of phase transitions in terms of disorder parameters. These indicate the presence of line-like excitations such as <a href="/wiki/Quantum_vortex" title="Quantum vortex">vortex</a>- or <a href="/wiki/Topological_defect" title="Topological defect">defect</a> lines. </p> <div class="mw-heading mw-heading3"><h3 id="Relevance_in_cosmology">Relevance in cosmology</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Phase_transition&action=edit&section=15" title="Edit section: Relevance in cosmology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Symmetry-breaking phase transitions play an important role in <a href="/wiki/Physical_cosmology" title="Physical cosmology">cosmology</a>. As the universe expanded and cooled, the vacuum underwent a series of symmetry-breaking phase transitions. For example, the electroweak transition broke the SU(2)×U(1) symmetry of the <a href="/wiki/Electroweak_force" class="mw-redirect" title="Electroweak force">electroweak field</a> into the U(1) symmetry of the present-day <a href="/wiki/Electromagnetic_field" title="Electromagnetic field">electromagnetic field</a>. This transition is important to explain the asymmetry between the amount of matter and antimatter in the present-day universe, according to <a href="/wiki/Electroweak_baryogenesis" class="mw-redirect" title="Electroweak baryogenesis">electroweak baryogenesis</a> theory. </p><p>Progressive phase transitions in an expanding universe are implicated in the development of order in the universe, as is illustrated by the work of <a href="/wiki/Eric_Chaisson" title="Eric Chaisson">Eric Chaisson</a><sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/David_Layzer" title="David Layzer">David Layzer</a>.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> </p><p>See also <a href="/wiki/Relational_order_theories" class="mw-redirect" title="Relational order theories">relational order theories</a> and <a href="/wiki/Order_and_disorder" title="Order and disorder">order and disorder</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Critical_exponents_and_universality_classes">Critical exponents and universality classes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Phase_transition&action=edit&section=16" title="Edit section: Critical exponents and universality classes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Critical_exponent" title="Critical exponent">critical exponent</a></div> <p>Continuous phase transitions are easier to study than first-order transitions due to the absence of <a href="/wiki/Latent_heat" title="Latent heat">latent heat</a>, and they have been discovered to have many interesting properties. The phenomena associated with continuous phase transitions are called critical phenomena, due to their association with critical points. </p><p>Continuous phase transitions can be characterized by parameters known as <a href="/wiki/Critical_exponent" title="Critical exponent">critical exponents</a>. The most important one is perhaps the exponent describing the divergence of the thermal <a href="/wiki/Correlation_length" class="mw-redirect" title="Correlation length">correlation length</a> by approaching the transition. For instance, let us examine the behavior of the <a href="/wiki/Heat_capacity" title="Heat capacity">heat capacity</a> near such a transition. We vary the temperature <i>T</i> of the system while keeping all the other thermodynamic variables fixed and find that the transition occurs at some critical temperature <i>T</i><sub>c</sub>. When <i>T</i> is near <i>T</i><sub>c</sub>, the heat capacity <i>C</i> typically has a <a href="/wiki/Power_law" title="Power law">power law</a> behavior: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C\propto |T_{\text{c}}-T|^{-\alpha }.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo>∝</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>c</mtext> </mrow> </msub> <mo>−</mo> <mi>T</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>α</mi> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C\propto |T_{\text{c}}-T|^{-\alpha }.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3cc12cb76ed282041ce81eb5f178ddbb1f62fb5b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.165ex; height:3.176ex;" alt="{\displaystyle C\propto |T_{\text{c}}-T|^{-\alpha }.}"></span></dd></dl> <p>The heat capacity of amorphous materials has such a behaviour near the glass transition temperature where the universal critical exponent <i>α</i> = 0.59<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> A similar behavior, but with the exponent <i>ν</i> instead of <i>α</i>, applies for the correlation length. </p><p>The exponent <i>ν</i> is positive. This is different with <i>α</i>. Its actual value depends on the type of phase transition we are considering. </p><p>The critical exponents are not necessarily the same above and below the critical temperature. When a continuous symmetry is explicitly broken down to a discrete symmetry by irrelevant (in the renormalization group sense) anisotropies, then some exponents (such as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \gamma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a223c880b0ce3da8f64ee33c4f0010beee400b1a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.262ex; height:2.176ex;" alt="{\displaystyle \gamma }"></span>, the exponent of the susceptibility) are not identical.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> </p><p>For −1 < <i>α</i> < 0, the heat capacity has a "kink" at the transition temperature. This is the behavior of liquid helium at the <a href="/wiki/Lambda_transition" title="Lambda transition">lambda transition</a> from a normal state to the <a href="/wiki/Superfluid" class="mw-redirect" title="Superfluid">superfluid</a> state, for which experiments have found <i>α</i> = −0.013 ± 0.003. At least one experiment was performed in the zero-gravity conditions of an orbiting satellite to minimize pressure differences in the sample.<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> This experimental value of α agrees with theoretical predictions based on <a href="/wiki/Variational_perturbation_theory" title="Variational perturbation theory">variational perturbation theory</a>.<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> </p><p>For 0 < <i>α</i> < 1, the heat capacity diverges at the transition temperature (though, since <i>α</i> < 1, the enthalpy stays finite). An example of such behavior is the 3D ferromagnetic phase transition. In the three-dimensional <a href="/wiki/Ising_model" title="Ising model">Ising model</a> for uniaxial magnets, detailed theoretical studies have yielded the exponent <i>α</i> ≈ +0.110. </p><p>Some model systems do not obey a power-law behavior. For example, mean field theory predicts a finite discontinuity of the heat capacity at the transition temperature, and the two-dimensional Ising model has a <a href="/wiki/Logarithm" title="Logarithm">logarithmic</a> divergence. However, these systems are limiting cases and an exception to the rule. Real phase transitions exhibit power-law behavior. </p><p>Several other critical exponents, <i>β</i>, <i>γ</i>, <i>δ</i>, <i>ν</i>, and <i>η</i>, are defined, examining the power law behavior of a measurable physical quantity near the phase transition. Exponents are related by scaling relations, such as </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta =\gamma /(\delta -1),\quad \nu =\gamma /(2-\eta ).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> <mo>=</mo> <mi>γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mo stretchy="false">(</mo> <mi>δ</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>,</mo> <mspace width="1em" /> <mi>ν</mi> <mo>=</mo> <mi>γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mo>−</mo> <mi>η</mi> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta =\gamma /(\delta -1),\quad \nu =\gamma /(2-\eta ).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68afaf2ed909973f623fe62b393a922c95c244cf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:31.456ex; height:2.843ex;" alt="{\displaystyle \beta =\gamma /(\delta -1),\quad \nu =\gamma /(2-\eta ).}"></span></dd></dl> <p>It can be shown that there are only two independent exponents, e.g. <i>ν</i> and <i>η</i>. </p><p>It is a remarkable fact that phase transitions arising in different systems often possess the same set of critical exponents. This phenomenon is known as <i>universality</i>. For example, the critical exponents at the liquid–gas critical point have been found to be independent of the chemical composition of the fluid. </p><p>More impressively, but understandably from above, they are an exact match for the critical exponents of the ferromagnetic phase transition in uniaxial magnets. Such systems are said to be in the same universality class. Universality is a prediction of the <a href="/wiki/Renormalization_group" title="Renormalization group">renormalization group</a> theory of phase transitions, which states that the thermodynamic properties of a system near a phase transition depend only on a small number of features, such as dimensionality and symmetry, and are insensitive to the underlying microscopic properties of the system. Again, the divergence of the correlation length is the essential point. </p> <div class="mw-heading mw-heading3"><h3 id="Critical_phenomena">Critical phenomena</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Phase_transition&action=edit&section=17" title="Edit section: Critical phenomena"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>There are also other critical phenomena; e.g., besides <i>static functions</i> there is also <i>critical dynamics</i>. As a consequence, at a phase transition one may observe <i>critical slowing down</i> or <i>speeding up</i>. Connected to the previous phenomenon is also the phenomenon of <i>enhanced fluctuations</i> before the phase transition, as a consequence of lower degree of stability of the initial phase of the system. The large <i>static universality classes</i> of a continuous phase transition split into smaller <i>dynamic universality</i> classes. In addition to the critical exponents, there are also universal relations for certain static or dynamic functions of the magnetic fields and temperature differences from the critical value.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (November 2023)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading3"><h3 id="Phase_transitions_in_biological_systems">Phase transitions in biological systems</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Phase_transition&action=edit&section=18" title="Edit section: Phase transitions in biological systems"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Phase transitions play many important roles in biological systems. Examples include the <a href="/wiki/Lipid_bilayer" title="Lipid bilayer">lipid bilayer</a> formation, the <a href="/wiki/Coil%E2%80%93globule_transition" title="Coil–globule transition">coil-globule transition</a> in the process of <a href="/wiki/Protein_folding" title="Protein folding">protein folding</a> and <a href="/wiki/DNA_melting" class="mw-redirect" title="DNA melting">DNA melting</a>, liquid crystal-like transitions in the process of <a href="/wiki/DNA_condensation" title="DNA condensation">DNA condensation</a>, and cooperative ligand binding to DNA and proteins with the character of phase transition.<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> </p><p>In <i>biological membranes</i>, gel to liquid crystalline phase transitions play a critical role in physiological functioning of biomembranes. In gel phase, due to low fluidity of membrane lipid fatty-acyl chains, membrane proteins have restricted movement and thus are restrained in exercise of their physiological role. Plants depend critically on photosynthesis by <a href="/wiki/Chloroplast" title="Chloroplast">chloroplast</a> <a href="/wiki/Thylakoid_membrane" class="mw-redirect" title="Thylakoid membrane">thylakoid membranes</a> which are exposed cold environmental temperatures. Thylakoid membranes retain innate fluidity even at relatively low temperatures because of high degree of fatty-acyl disorder allowed by their high content of <a href="/wiki/Linolenic_acid" title="Linolenic acid">linolenic acid</a>, 18-carbon chain with 3-double bonds.<sup id="cite_ref-YashRoy_1987_38-0" class="reference"><a href="#cite_note-YashRoy_1987-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> Gel-to-liquid crystalline phase transition temperature of biological membranes can be determined by many techniques including calorimetry, fluorescence, <a href="/wiki/Spin_label" title="Spin label">spin label</a> <a href="/wiki/Electron_paramagnetic_resonance" title="Electron paramagnetic resonance">electron paramagnetic resonance</a> and <a href="/wiki/NMR" class="mw-redirect" title="NMR">NMR</a> by recording measurements of the concerned parameter by at series of sample temperatures. A simple method for its determination from 13-C NMR line intensities has also been proposed.<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> </p><p>It has been proposed that some biological systems might lie near critical points. Examples include <a href="/wiki/Neural_network_(biology)" title="Neural network (biology)">neural networks</a> in the salamander retina,<sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> bird flocks<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> gene expression networks in Drosophila,<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> and protein folding.<sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> However, it is not clear whether or not alternative reasons could explain some of the phenomena supporting arguments for criticality.<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> It has also been suggested that biological organisms share two key properties of phase transitions: the change of macroscopic behavior and the coherence of a system at a critical point.<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> Phase transitions are prominent feature of motor behavior in biological systems.<sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> Spontaneous gait transitions,<sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> as well as fatigue-induced motor task disengagements,<sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> show typical critical behavior as an intimation of the sudden qualitative change of the previously stable motor behavioral pattern. </p><p>The characteristic feature of second order phase transitions is the appearance of <a href="/wiki/Fractal" title="Fractal">fractals</a> in some <a href="/wiki/Scale-free_network" title="Scale-free network">scale-free</a> properties. It has long been known that protein globules are shaped by interactions with water. There are 20 amino acids that form side groups on protein peptide chains range from <a href="/wiki/Hydrophilic" class="mw-redirect" title="Hydrophilic">hydrophilic</a> to hydrophobic, causing the former to lie near the globular surface, while the latter lie closer to the globular center. Twenty fractals were discovered in solvent associated surface areas of > 5000 protein segments.<sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> The existence of these fractals proves that proteins function near critical points of second-order phase transitions. </p><p>In groups of organisms in stress (when approaching critical transitions), correlations tend to increase, while at the same time, fluctuations also increase. This effect is supported by many experiments and observations of groups of people, mice, trees, and grassy plants.<sup id="cite_ref-50" class="reference"><a href="#cite_note-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Phase_transitions_in_social_systems">Phase transitions in social systems</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Phase_transition&action=edit&section=19" title="Edit section: Phase transitions in social systems"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Complex_system_approach_to_peace_and_armed_conflict#Phase_transitions" title="Complex system approach to peace and armed conflict">Complex system approach to peace and armed conflict § Phase transitions</a></div> <p>Phase transitions have been hypothesised to occur in social systems viewed as dynamical systems. A hypothesis proposed in the 1990s and 2000s in the context of <a href="/wiki/Complex_system_approach_to_peace_and_armed_conflict#Phase_transitions" title="Complex system approach to peace and armed conflict">peace and armed conflict</a> is that when a conflict that is non-violent shifts to a phase of armed conflict, this is a phase transition from latent to manifest phases within the dynamical system.<sup id="cite_ref-Hendricks2009_complexity_theory_51-0" class="reference"><a href="#cite_note-Hendricks2009_complexity_theory-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 49">: 49 </span></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Experimental">Experimental</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Phase_transition&action=edit&section=20" title="Edit section: Experimental"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A variety of methods are applied for studying the various effects. Selected examples are: </p> <ul><li><a href="/wiki/Hall_effect" title="Hall effect">Hall effect</a> (measurement of magnetic transitions)</li> <li><a href="/wiki/M%C3%B6ssbauer_spectroscopy" title="Mössbauer spectroscopy">Mössbauer spectroscopy</a> (simultaneous measurement of magnetic and non-magnetic transitions. Limited up to about 800–1000 °C)</li> <li><a href="/wiki/Neutron_diffraction" title="Neutron diffraction">Neutron diffraction</a></li> <li><a href="/wiki/Perturbed_angular_correlation" title="Perturbed angular correlation">Perturbed angular correlation</a> (simultaneous measurement of magnetic and non-magnetic transitions. No temperature limits. Over 2000 °C already performed, theoretical possible up to the highest crystal material, such as <a href="/wiki/Tantalum_hafnium_carbide" title="Tantalum hafnium carbide">tantalum hafnium carbide</a> 4215 °C.)</li> <li><a href="/wiki/Raman_Spectroscopy" class="mw-redirect" title="Raman Spectroscopy">Raman Spectroscopy</a></li> <li><a href="/wiki/SQUID" title="SQUID">SQUID</a> (measurement of magnetic transitions)</li> <li><a href="/wiki/Thermogravimetry" class="mw-redirect" title="Thermogravimetry">Thermogravimetry</a> (very common)</li> <li><a href="/wiki/X-ray_diffraction" title="X-ray diffraction">X-ray diffraction</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Phase_transition&action=edit&section=21" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col"> <ul><li><a href="/wiki/Allotropy" title="Allotropy">Allotropy</a> – Property of some chemical elements to exist in two or more different forms</li> <li><a href="/wiki/Autocatalytic_reactions_and_order_creation" class="mw-redirect" title="Autocatalytic reactions and order creation">Autocatalytic reactions and order creation</a> – Chemical reaction whose product is also its catalyst<span style="display:none" class="category-annotation-with-redirected-description">Pages displaying short descriptions of redirect targets</span></li> <li><a href="/wiki/Crystal_growth" title="Crystal growth">Crystal growth</a> – Major stage of a crystallization process <ul><li><a href="/wiki/Abnormal_grain_growth" title="Abnormal grain growth">Abnormal grain growth</a> – Phenomenon of certain material grains growing faster than others</li></ul></li> <li><a href="/wiki/Differential_scanning_calorimetry" title="Differential scanning calorimetry">Differential scanning calorimetry</a> – Thermoanalytical technique</li> <li><a href="/wiki/Diffusionless_transformations" class="mw-redirect" title="Diffusionless transformations">Diffusionless transformations</a> – Shift of atomic positions in a crystal structure<span style="display:none" class="category-annotation-with-redirected-description">Pages displaying short descriptions of redirect targets</span></li> <li><a href="/wiki/Ehrenfest_equations" title="Ehrenfest equations">Ehrenfest equations</a></li> <li><a href="/wiki/Ising_Model" class="mw-redirect" title="Ising Model">Ising Model</a> – Mathematical model of ferromagnetism in statistical mechanics<span style="display:none" class="category-annotation-with-redirected-description">Pages displaying short descriptions of redirect targets</span></li> <li><a href="/wiki/Jamming_(physics)" title="Jamming (physics)">Jamming (physics)</a> – physical process by which the viscosity of some mesoscopic materials, such as granular materials, glasses, foams, polymers, emulsions, and other complex fluids, increases with increasing particle density<span style="display:none" class="category-wikidata-fallback-annotation">Pages displaying wikidata descriptions as a fallback</span></li> <li><a href="/wiki/Kelvin_probe_force_microscope" title="Kelvin probe force microscope">Kelvin probe force microscope</a> – Noncontact variant of atomic force microscopy</li> <li><a href="/wiki/Landau_theory" title="Landau theory">Landau theory</a> – Theory of continuous phase transitions of second order phase transitions</li> <li><a href="/wiki/Laser-heated_pedestal_growth" title="Laser-heated pedestal growth">Laser-heated pedestal growth</a> – crystal growth technique<span style="display:none" class="category-wikidata-fallback-annotation">Pages displaying wikidata descriptions as a fallback</span></li> <li><a href="/wiki/List_of_states_of_matter" title="List of states of matter">List of states of matter</a> – Different known phase of states matter</li> <li><a href="/wiki/Micro-pulling-down" title="Micro-pulling-down">Micro-pulling-down</a> – Crystal growth technique</li> <li><a href="/wiki/Percolation_theory" title="Percolation theory">Percolation theory</a> – Mathematical theory on behavior of connected clusters in a random graph <ul><li><a href="/wiki/Continuum_percolation_theory" title="Continuum percolation theory">Continuum percolation theory</a></li></ul></li> <li><a href="/wiki/Superfluid_film" title="Superfluid film">Superfluid film</a> – Thin layer of liquid in a superfluid state</li> <li><a href="/wiki/Superradiant_phase_transition" title="Superradiant phase transition">Superradiant phase transition</a> – Process in quantum optics</li> <li><a href="/wiki/Topological_quantum_field_theory" title="Topological quantum field theory">Topological quantum field theory</a> – Field theory involving topological effects in physics</li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Phase_transition&action=edit&section=22" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output 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a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and 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class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:276956">276956</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physica+A%3A+Statistical+Mechanics+and+Its+Applications&rft.atitle=Correlations%2C+risk+and+crisis%3A+From+physiology+to+finance&rft.volume=389&rft.issue=16&rft.pages=3193-3217&rft.date=2010-08&rft_id=info%3Aarxiv%2F0905.0129&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A276956%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1016%2Fj.physa.2010.03.035&rft_id=info%3Abibcode%2F2010PhyA..389.3193G&rft.aulast=Gorban&rft.aufirst=A.N.&rft.au=Smirnova%2C+E.V.&rft.au=Tyukina%2C+T.A.&rft_id=https%3A%2F%2Fwww.researchgate.net%2Fpublication%2F222687003&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhase+transition" class="Z3988"></span></span> </li> <li id="cite_note-Hendricks2009_complexity_theory-51"><span class="mw-cite-backlink"><b><a href="#cite_ref-Hendricks2009_complexity_theory_51-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDiane_Hendrick2009" class="citation cs2">Diane Hendrick (June 2009), <a rel="nofollow" class="external text" href="https://www.beyondintractability.org/bi_affiliated_projects/dsap/publications/complexity-theory-transformation-hendrick.pdf"><i>Complexity Theory and Conflict Transformation: An Exploration of Potential and Implications</i></a> <span class="cs1-format">(PDF)</span>, <a href="/wiki/Department_of_Peace_Studies,_University_of_Bradford" title="Department of Peace Studies, University of Bradford">Department of Peace Studies, University of Bradford</a>, <a href="/wiki/WDQ_(identifier)" class="mw-redirect" title="WDQ (identifier)">Wikidata</a> <a href="https://www.wikidata.org/wiki/Q126669745" class="extiw" title="d:Q126669745">Q126669745</a>, <a rel="nofollow" class="external text" href="https://web.archive.org/web/20221126031844/https://www.beyondintractability.org/bi_affiliated_projects/dsap/publications/complexity-theory-transformation-hendrick.pdf">archived</a> <span class="cs1-format">(PDF)</span> from the original on 26 November 2022</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Complexity+Theory+and+Conflict+Transformation%3A+An+Exploration+of+Potential+and+Implications&rft.pub=Department+of+Peace+Studies%2C+University+of+Bradford&rft.date=2009-06&rft.au=Diane+Hendrick&rft_id=https%3A%2F%2Fwww.beyondintractability.org%2Fbi_affiliated_projects%2Fdsap%2Fpublications%2Fcomplexity-theory-transformation-hendrick.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhase+transition" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Phase_transition&action=edit&section=23" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Philip_Warren_Anderson" class="mw-redirect" title="Philip Warren Anderson">Anderson, P.W.</a>, <i>Basic Notions of Condensed Matter Physics</i>, <a href="/wiki/Perseus_Publishing" class="mw-redirect" title="Perseus Publishing">Perseus Publishing</a> (1997).</li> <li><a href="/wiki/Amir_Faghri" title="Amir Faghri">Faghri, A.</a>, and <a href="/wiki/Yuwen_Zhang" title="Yuwen Zhang">Zhang, Y.</a>, <a rel="nofollow" class="external text" href="https://www.springer.com/gp/book/9783030221362">Fundamentals of Multiphase Heat Transfer and Flow</a>, <a href="/wiki/Springer_Nature" title="Springer Nature">Springer Nature</a> Switzerland AG, 2020.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFisher1974" class="citation journal cs1"><a href="/wiki/Michael_E._Fisher" class="mw-redirect" title="Michael E. Fisher">Fisher, M.E.</a> (1974). "The renormalization group in the theory of critical behavior". <i>Rev. Mod. Phys</i>. <b>46</b> (4): 597–616. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1974RvMP...46..597F">1974RvMP...46..597F</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2Frevmodphys.46.597">10.1103/revmodphys.46.597</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Rev.+Mod.+Phys.&rft.atitle=The+renormalization+group+in+the+theory+of+critical+behavior&rft.volume=46&rft.issue=4&rft.pages=597-616&rft.date=1974&rft_id=info%3Adoi%2F10.1103%2Frevmodphys.46.597&rft_id=info%3Abibcode%2F1974RvMP...46..597F&rft.aulast=Fisher&rft.aufirst=M.E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhase+transition" class="Z3988"></span></li> <li>Goldenfeld, N., <i>Lectures on Phase Transitions and the Renormalization Group</i>, Perseus Publishing (1992).</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFIvancevic,_Vladimir_GIvancevic,_Tijana_T2008" class="citation cs2">Ivancevic, Vladimir G; Ivancevic, Tijana T (2008), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=wpsPgHgtxEYC&q=complex+nonlinearity"><i>Chaos, Phase Transitions, Topology Change and Path Integrals</i></a>, Berlin: Springer, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-79356-4" title="Special:BookSources/978-3-540-79356-4"><bdi>978-3-540-79356-4</bdi></a><span class="reference-accessdate">, retrieved <span class="nowrap">14 March</span> 2013</span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chaos%2C+Phase+Transitions%2C+Topology+Change+and+Path+Integrals&rft.place=Berlin&rft.pub=Springer&rft.date=2008&rft.isbn=978-3-540-79356-4&rft.au=Ivancevic%2C+Vladimir+G&rft.au=Ivancevic%2C+Tijana+T&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DwpsPgHgtxEYC%26q%3Dcomplex%2Bnonlinearity&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhase+transition" class="Z3988"></span></li> <li>M.R. Khoshbin-e-Khoshnazar, <a rel="nofollow" class="external text" href="http://www.physedu.in/uploads/publication/23/371/4.-Ice-Phase-transition-as-a-sample-of-finite-system-phase--transition.pdf"><i>Ice Phase Transition as a sample of finite system phase transition</i>, (Physics Education (India) Volume 32. No. 2, Apr - Jun 2016) </a></li> <li><a href="/wiki/Hagen_Kleinert" title="Hagen Kleinert">Kleinert, H.</a>, <i>Gauge Fields in Condensed Matter</i>, Vol. I, "<a href="/wiki/Superfluidity" title="Superfluidity">Superfluidity</a> and <a href="/wiki/Vortex" title="Vortex">Vortex lines</a>; Disorder Fields, <a href="/wiki/Phase_Transition" class="mw-redirect" title="Phase Transition">Phase Transitions</a>", pp. 1–742, <a rel="nofollow" class="external text" href="https://archive.today/20060514143926/http://www.worldscibooks.com/physics/0356.htm">World Scientific (Singapore, 1989)</a>; Paperback <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9971-5-0210-0" title="Special:BookSources/9971-5-0210-0">9971-5-0210-0</a> (<a rel="nofollow" class="external text" href="http://www.physik.fu-berlin.de/~kleinert/kleiner_reb1/contents1.html">physik.fu-berlin.de readable online</a>)</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKleinertVerena_Schulte-Frohlinde2001" class="citation book cs1"><a href="/wiki/Hagen_Kleinert" title="Hagen Kleinert">Kleinert, Hagen</a>; Verena Schulte-Frohlinde (2001). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080226151023/http://www.worldscibooks.com/physics/4733.html"><i>Critical Properties of φ<sup>4</sup>-Theories</i></a>. World Scientific. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/981-02-4659-5" title="Special:BookSources/981-02-4659-5"><bdi>981-02-4659-5</bdi></a>. Archived from <a rel="nofollow" class="external text" href="http://www.worldscibooks.com/physics/4733.html">the original</a> on 26 February 2008.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Critical+Properties+of+%CF%86%3Csup%3E4%3C%2Fsup%3E-Theories&rft.pub=World+Scientific&rft.date=2001&rft.isbn=981-02-4659-5&rft.aulast=Kleinert&rft.aufirst=Hagen&rft.au=Verena+Schulte-Frohlinde&rft_id=http%3A%2F%2Fwww.worldscibooks.com%2Fphysics%2F4733.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhase+transition" class="Z3988"></span> (<a rel="nofollow" class="external text" href="http://www.physik.fu-berlin.de/~kleinert/b8">readable online</a>).</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKogutWilson1974" class="citation journal cs1">Kogut, J.; <a href="/wiki/Kenneth_G._Wilson" title="Kenneth G. Wilson">Wilson, K</a> (1974). "The Renormalization Group and the epsilon-Expansion". <i>Phys. Rep</i>. <b>12</b> (2): 75–199. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1974PhR....12...75W">1974PhR....12...75W</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0370-1573%2874%2990023-4">10.1016/0370-1573(74)90023-4</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Phys.+Rep.&rft.atitle=The+Renormalization+Group+and+the+epsilon-Expansion&rft.volume=12&rft.issue=2&rft.pages=75-199&rft.date=1974&rft_id=info%3Adoi%2F10.1016%2F0370-1573%2874%2990023-4&rft_id=info%3Abibcode%2F1974PhR....12...75W&rft.aulast=Kogut&rft.aufirst=J.&rft.au=Wilson%2C+K&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhase+transition" class="Z3988"></span></li> <li><a href="/wiki/Martin_H._Krieger" title="Martin H. Krieger">Krieger, Martin H.</a>, <i>Constitutions of matter : mathematically modelling the most everyday of physical phenomena</i>, <a href="/wiki/University_of_Chicago_Press" title="University of Chicago Press">University of Chicago Press</a>, 1996. Contains a detailed pedagogical discussion of <a href="/wiki/Lars_Onsager" title="Lars Onsager">Onsager</a>'s solution of the 2-D Ising Model.</li> <li><a href="/wiki/Lev_Davidovich_Landau" class="mw-redirect" title="Lev Davidovich Landau">Landau, L.D.</a> and <a href="/wiki/Evgeny_Mikhailovich_Lifshitz" class="mw-redirect" title="Evgeny Mikhailovich Lifshitz">Lifshitz, E.M.</a>, <i>Statistical Physics Part 1</i>, vol. 5 of <i><a href="/wiki/Course_of_Theoretical_Physics" title="Course of Theoretical Physics">Course of Theoretical Physics</a></i>, Pergamon Press, 3rd Ed. (1994).</li> <li>Mussardo G., "Statistical Field Theory. An Introduction to Exactly Solved Models of Statistical Physics", Oxford University Press, 2010.</li> <li><a href="/wiki/Manfred_R._Schroeder" title="Manfred R. Schroeder">Schroeder, Manfred R.</a>, <i>Fractals, chaos, power laws : minutes from an infinite paradise</i>, New York: <a href="/wiki/W._H._Freeman" class="mw-redirect" title="W. H. Freeman">W. H. Freeman</a>, 1991. Very well-written book in "semi-popular" style—not a textbook—aimed at an audience with some training in mathematics and the physical sciences. Explains what scaling in phase transitions is all about, among other things.</li> <li><a href="/wiki/H._Eugene_Stanley" title="H. Eugene Stanley">H. E. Stanley</a>, <i>Introduction to Phase Transitions and Critical Phenomena</i> (Oxford University Press, Oxford and New York 1971).</li> <li><a href="/wiki/Julia_Yeomans" title="Julia Yeomans">Yeomans J. M.</a>, <i>Statistical Mechanics of Phase Transitions</i>, Oxford University Press, 1992.</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Phase_transition&action=edit&section=24" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> Media related to <a href="https://commons.wikimedia.org/wiki/Category:Phase_changes" class="extiw" title="commons:Category:Phase changes">Phase changes</a> at Wikimedia Commons </p> <ul><li><a rel="nofollow" class="external text" href="http://www.ibiblio.org/e-notes/Perc/contents.htm">Interactive Phase Transitions on lattices</a> with Java applets</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20160204235430/http://www.sklogwiki.org/SklogWiki/index.php/Universality_classes">Universality classes</a> from Sklogwiki</li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output 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autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:States_of_matter" title="Template:States of matter"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:States_of_matter" title="Template talk:States of matter"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:States_of_matter" title="Special:EditPage/Template:States of matter"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="States_of_matter_(list)" style="font-size:114%;margin:0 4em"><a href="/wiki/State_of_matter" title="State of matter">States of matter</a> (<a href="/wiki/List_of_states_of_matter" title="List of states of matter">list</a>)</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">State</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Solid" title="Solid">Solid</a></li> <li><a href="/wiki/Liquid" title="Liquid">Liquid</a></li> <li><a href="/wiki/Gas" title="Gas">Gas</a> / <a href="/wiki/Vapor" title="Vapor">Vapor</a></li> <li><a href="/wiki/Supercritical_fluid" title="Supercritical fluid">Supercritical fluid</a></li> <li><a href="/wiki/Plasma_(physics)" title="Plasma (physics)">Plasma</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="7" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:Phase_change_-_en.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Phase_change_-_en.svg/150px-Phase_change_-_en.svg.png" decoding="async" width="150" height="159" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Phase_change_-_en.svg/225px-Phase_change_-_en.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Phase_change_-_en.svg/300px-Phase_change_-_en.svg.png 2x" data-file-width="493" data-file-height="524" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Low energy</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bose%E2%80%93Einstein_condensate" title="Bose–Einstein condensate">Bose–Einstein condensate</a></li> <li><a href="/wiki/Fermionic_condensate" title="Fermionic condensate">Fermionic condensate</a></li> <li><a href="/wiki/Degenerate_matter" title="Degenerate matter">Degenerate matter</a></li> <li><a href="/wiki/Quantum_Hall_effect" title="Quantum Hall effect">Quantum Hall</a></li> <li><a href="/wiki/Rydberg_matter" title="Rydberg matter">Rydberg matter</a></li> <li><a href="/wiki/Strange_matter" title="Strange matter">Strange matter</a></li> <li><a href="/wiki/Superfluidity" title="Superfluidity">Superfluid</a></li> <li><a href="/wiki/Supersolid" title="Supersolid">Supersolid</a></li> <li><a href="/wiki/Photonic_molecule" title="Photonic molecule">Photonic molecule</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">High energy</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/QCD_matter" title="QCD matter">QCD matter</a></li> <li><a href="/wiki/Quark%E2%80%93gluon_plasma" title="Quark–gluon plasma">Quark–gluon plasma</a></li> <li><a href="/wiki/Color-glass_condensate" title="Color-glass condensate">Color-glass condensate</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other states</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Colloid" title="Colloid">Colloid</a></li> <li><a href="/wiki/Crystal" title="Crystal">Crystal</a></li> <li><a href="/wiki/Liquid_crystal" title="Liquid crystal">Liquid crystal</a></li> <li><a href="/wiki/Time_crystal" title="Time crystal">Time crystal</a></li> <li><a href="/wiki/Quantum_spin_liquid" title="Quantum spin liquid">Quantum spin liquid</a></li> <li><a href="/wiki/Exotic_matter" title="Exotic matter">Exotic matter</a></li> <li><a href="/wiki/Programmable_matter" title="Programmable matter">Programmable matter</a></li> <li><a href="/wiki/Dark_matter" title="Dark matter">Dark matter</a></li> <li><a href="/wiki/Antimatter" title="Antimatter">Antimatter</a></li> <li>Magnetically ordered <ul><li><a href="/wiki/Antiferromagnetism" title="Antiferromagnetism">Antiferromagnet</a></li> <li><a href="/wiki/Ferrimagnetism" title="Ferrimagnetism">Ferrimagnet</a></li> <li><a href="/wiki/Ferromagnetism" title="Ferromagnetism">Ferromagnet</a></li></ul></li> <li><a href="/wiki/String-net_liquid" title="String-net liquid">String-net liquid</a></li> <li><a href="/wiki/Superglass" title="Superglass">Superglass</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Phase_transitions" class="mw-redirect" title="Phase transitions">Phase transitions</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Boiling" title="Boiling">Boiling</a></li> <li><a href="/wiki/Boiling_point" title="Boiling point">Boiling point</a></li> <li><a href="/wiki/Condensation" title="Condensation">Condensation</a></li> <li><a href="/wiki/Critical_line_(thermodynamics)" title="Critical line (thermodynamics)">Critical line</a></li> <li><a href="/wiki/Critical_point_(thermodynamics)" title="Critical point (thermodynamics)">Critical point</a></li> <li><a href="/wiki/Crystallization" title="Crystallization">Crystallization</a></li> <li><a href="/wiki/Deposition_(phase_transition)" title="Deposition (phase transition)">Deposition</a></li> <li><a href="/wiki/Evaporation" title="Evaporation">Evaporation</a></li> <li><a href="/wiki/Flash_evaporation" title="Flash evaporation">Flash evaporation</a></li> <li><a href="/wiki/Freezing" title="Freezing">Freezing</a></li> <li><a href="/wiki/Chemical_ionization" title="Chemical ionization">Chemical ionization</a></li> <li><a href="/wiki/Ionization" title="Ionization">Ionization</a></li> <li><a href="/wiki/Lambda_point" title="Lambda point">Lambda point</a></li> <li><a href="/wiki/Melting" title="Melting">Melting</a></li> <li><a href="/wiki/Melting_point" title="Melting point">Melting point</a></li> <li><a href="/wiki/Plasma_recombination" title="Plasma recombination">Recombination</a></li> <li><a href="/wiki/Regelation" title="Regelation">Regelation</a></li> <li><a href="/wiki/Vapor%E2%80%93liquid_equilibrium" title="Vapor–liquid equilibrium">Saturated fluid</a></li> <li><a href="/wiki/Sublimation_(phase_transition)" title="Sublimation (phase transition)">Sublimation</a></li> <li><a href="/wiki/Supercooling" title="Supercooling">Supercooling</a></li> <li><a href="/wiki/Triple_point" title="Triple point">Triple point</a></li> <li><a href="/wiki/Vaporization" title="Vaporization">Vaporization</a></li> <li><a href="/wiki/Vitrification" title="Vitrification">Vitrification</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Quantities</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Enthalpy_of_fusion" title="Enthalpy of fusion">Enthalpy of fusion</a></li> <li><a href="/wiki/Enthalpy_of_sublimation" title="Enthalpy of sublimation">Enthalpy of sublimation</a></li> <li><a href="/wiki/Enthalpy_of_vaporization" title="Enthalpy of vaporization">Enthalpy of vaporization</a></li> <li><a href="/wiki/Latent_heat" title="Latent heat">Latent heat</a></li> <li><a href="/wiki/Latent_internal_energy" title="Latent internal energy">Latent internal energy</a></li> <li><a href="/wiki/Trouton%27s_rule" title="Trouton's rule">Trouton's rule</a></li> <li><a href="/wiki/Volatility_(chemistry)" title="Volatility (chemistry)">Volatility</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Baryonic_matter" class="mw-redirect" title="Baryonic matter">Baryonic matter</a></li> <li><a href="/wiki/Binodal" title="Binodal">Binodal</a></li> <li><a href="/wiki/Compressed_fluid" title="Compressed fluid">Compressed fluid</a></li> <li><a href="/wiki/Cooling_curve" title="Cooling curve">Cooling curve</a></li> <li><a href="/wiki/Equation_of_state" title="Equation of state">Equation of state</a></li> <li><a href="/wiki/Leidenfrost_effect" title="Leidenfrost effect">Leidenfrost effect</a></li> <li><a href="/wiki/Macroscopic_quantum_phenomena" title="Macroscopic quantum phenomena">Macroscopic quantum phenomena</a></li> <li><a href="/wiki/Mpemba_effect" title="Mpemba effect">Mpemba effect</a></li> <li><a href="/wiki/Order_and_disorder_(physics)" class="mw-redirect" title="Order and disorder (physics)">Order and disorder (physics)</a></li> <li><a href="/wiki/Spinodal" title="Spinodal">Spinodal</a></li> <li><a href="/wiki/Superconductivity" title="Superconductivity">Superconductivity</a></li> <li><a href="/wiki/Superheated_water" title="Superheated water">Superheated vapor</a></li> <li><a href="/wiki/Superheating" title="Superheating">Superheating</a></li> <li><a href="/wiki/Thermo-dielectric_effect" title="Thermo-dielectric effect">Thermo-dielectric effect</a></li></ul> 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