CINXE.COM

<!DOCTYPE html> <html > <head> <meta charset="utf-8"> <meta rel="search" type="application/opensearchdescription+xml" href="/open_search.xml" title="Academia.edu"> <meta content="width=device-width, initial-scale=1" name="viewport"> <meta name="google-site-verification" content="bKJMBZA7E43xhDOopFZkssMMkBRjvYERV-NaN4R6mrs"> <meta name="csrf-param" content="authenticity_token" /> <meta name="csrf-token" content="3CKJMOeixLeNCQ+WfmDnFYLqOs9V/+jY1JwRJJFeD6chGHKn+ELQkhOjFr/FJhYW8GeVRvu5NKQzXY5X3atPNw==" /> <meta name="citation_title" content="Effects of ramification and connectivity degree on site percolation threshold on regular lattices and fractal networks" /> <meta name="citation_publication_date" content="2019/03/01" /> <meta name="citation_journal_title" content="Physics Letters" /> <meta name="citation_author" content="Alexander Balankin" /> <meta name="twitter:card" content="summary" /> <meta name="twitter:url" content="https://www.academia.edu/112693131/Effects_of_ramification_and_connectivity_degree_on_site_percolation_threshold_on_regular_lattices_and_fractal_networks" /> <meta name="twitter:title" content="Effects of ramification and connectivity degree on site percolation threshold on regular lattices and fractal networks" /> <meta name="twitter:description" content="Academia.edu is a platform for academics to share research papers." /> <meta name="twitter:image" content="https://0.academia-photos.com/31879133/53408813/41535800/s200_alexander.balankin.gif" /> <meta property="fb:app_id" content="2369844204" /> <meta property="og:type" content="article" /> <meta property="og:url" content="https://www.academia.edu/112693131/Effects_of_ramification_and_connectivity_degree_on_site_percolation_threshold_on_regular_lattices_and_fractal_networks" /> <meta property="og:title" content="Effects of ramification and connectivity degree on site percolation threshold on regular lattices and fractal networks" /> <meta property="og:image" content="http://a.academia-assets.com/images/open-graph-icons/fb-paper.gif" /> <meta property="og:description" content="Effects of ramification and connectivity degree on site percolation threshold on regular lattices and fractal networks" /> <meta property="article:author" content="https://independent.academia.edu/AlexanderBalankin" /> <meta name="description" content="Effects of ramification and connectivity degree on site percolation threshold on regular lattices and fractal networks" /> <title>(PDF) Effects of ramification and connectivity degree on site percolation threshold on regular lattices and fractal networks | Alexander Balankin - Academia.edu</title> <link rel="canonical" href="https://www.academia.edu/112693131/Effects_of_ramification_and_connectivity_degree_on_site_percolation_threshold_on_regular_lattices_and_fractal_networks" /> <script async src="https://www.googletagmanager.com/gtag/js?id=G-5VKX33P2DS"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-5VKX33P2DS', { cookie_domain: 'academia.edu', send_page_view: false, }); gtag('event', 'page_view', { 'controller': "single_work", 'action': "show", 'controller_action': 'single_work#show', 'logged_in': 'false', 'edge': 'unknown', // Send nil if there is no A/B test bucket, in case some records get logged // with missing data - that way we can distinguish between the two cases. // ab_test_bucket should be of the form <ab_test_name>:<bucket> 'ab_test_bucket': null, }) </script> <script> var $controller_name = 'single_work'; var $action_name = "show"; var $rails_env = 'production'; var $app_rev = '49879c2402910372f4abc62630a427bbe033d190'; var $domain = 'academia.edu'; var $app_host = "academia.edu"; var $asset_host = "academia-assets.com"; var $start_time = new Date().getTime(); var $recaptcha_key = "6LdxlRMTAAAAADnu_zyLhLg0YF9uACwz78shpjJB"; var $recaptcha_invisible_key = "6Lf3KHUUAAAAACggoMpmGJdQDtiyrjVlvGJ6BbAj"; var $disableClientRecordHit = false; </script> <script> window.require = { config: function() { return function() {} } } </script> <script> window.Aedu = window.Aedu || {}; window.Aedu.hit_data = null; window.Aedu.serverRenderTime = new Date(1732424463000); window.Aedu.timeDifference = new Date().getTime() - 1732424463000; </script> <script type="application/ld+json">{"@context":"https://schema.org","@type":"ScholarlyArticle","abstract":null,"author":[{"@context":"https://schema.org","@type":"Person","name":"Alexander Balankin"}],"contributor":[],"dateCreated":"2023-12-31","dateModified":null,"datePublished":"2019-03-01","headline":"Effects of ramification and connectivity degree on site percolation threshold on regular lattices and fractal networks","inLanguage":"en","keywords":["Physics","Statistical Physics","Mathematical Sciences","Physical sciences","Fractal","Percolation threshold","Percolation Theory","Degree in music","Physics Letters A"],"locationCreated":null,"publication":"Physics Letters","publisher":{"@context":"https://schema.org","@type":"Organization","name":"Elsevier BV"},"image":null,"thumbnailUrl":null,"url":"https://www.academia.edu/112693131/Effects_of_ramification_and_connectivity_degree_on_site_percolation_threshold_on_regular_lattices_and_fractal_networks","sourceOrganization":[{"@context":"https://schema.org","@type":"EducationalOrganization","name":null}]}</script><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/single_work_page/loswp-352e32ba4e89304dc0b4fa5b3952eef2198174c54cdb79066bc62e91c68a1a91.css" /><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system/body-8d679e925718b5e8e4b18e9a4fab37f7eaa99e43386459376559080ac8f2856a.css" /><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system/button-3cea6e0ad4715ed965c49bfb15dedfc632787b32ff6d8c3a474182b231146ab7.css" /><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system/text_button-73590134e40cdb49f9abdc8e796cc00dc362693f3f0f6137d6cf9bb78c318ce7.css" /><link crossorigin="" href="https://fonts.gstatic.com/" rel="preconnect" /><link href="https://fonts.googleapis.com/css2?family=DM+Sans:ital,opsz,wght@0,9..40,100..1000;1,9..40,100..1000&family=Gupter:wght@400;500;700&family=IBM+Plex+Mono:wght@300;400&family=Material+Symbols+Outlined:opsz,wght,FILL,GRAD@20,400,0,0&display=swap" rel="stylesheet" /><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system/common-10fa40af19d25203774df2d4a03b9b5771b45109c2304968038e88a81d1215c5.css" /> </head> <body> <div id='react-modal'></div> <div class="js-upgrade-ie-banner" style="display: none; text-align: center; padding: 8px 0; background-color: #ebe480;"><p style="color: #000; font-size: 12px; margin: 0 0 4px;">Academia.edu no longer supports Internet Explorer.</p><p style="color: #000; font-size: 12px; margin: 0;">To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to <a href="https://www.academia.edu/upgrade-browser">upgrade your browser</a>.</p></div><script>// Show this banner for all versions of IE if (!!window.MSInputMethodContext || /(MSIE)/.test(navigator.userAgent)) { document.querySelector('.js-upgrade-ie-banner').style.display = 'block'; }</script> <div class="bootstrap login"><div class="modal fade login-modal" id="login-modal"><div class="login-modal-dialog modal-dialog"><div class="modal-content"><div class="modal-header"><button class="close close" data-dismiss="modal" type="button"><span aria-hidden="true">×</span><span class="sr-only">Close</span></button><h4 class="modal-title text-center"><strong>Log In</strong></h4></div><div class="modal-body"><div class="row"><div class="col-xs-10 col-xs-offset-1"><button class="btn btn-fb btn-lg btn-block btn-v-center-content" id="login-facebook-oauth-button"><svg style="float: left; width: 19px; line-height: 1em; margin-right: .3em;" aria-hidden="true" focusable="false" data-prefix="fab" data-icon="facebook-square" class="svg-inline--fa fa-facebook-square fa-w-14" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512"><path fill="currentColor" d="M400 32H48A48 48 0 0 0 0 80v352a48 48 0 0 0 48 48h137.25V327.69h-63V256h63v-54.64c0-62.15 37-96.48 93.67-96.48 27.14 0 55.52 4.84 55.52 4.84v61h-31.27c-30.81 0-40.42 19.12-40.42 38.73V256h68.78l-11 71.69h-57.78V480H400a48 48 0 0 0 48-48V80a48 48 0 0 0-48-48z"></path></svg><small><strong>Log in</strong> with <strong>Facebook</strong></small></button><br /><button class="btn btn-google btn-lg btn-block btn-v-center-content" id="login-google-oauth-button"><svg style="float: left; width: 22px; line-height: 1em; margin-right: .3em;" aria-hidden="true" focusable="false" data-prefix="fab" data-icon="google-plus" class="svg-inline--fa fa-google-plus fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M256,8C119.1,8,8,119.1,8,256S119.1,504,256,504,504,392.9,504,256,392.9,8,256,8ZM185.3,380a124,124,0,0,1,0-248c31.3,0,60.1,11,83,32.3l-33.6,32.6c-13.2-12.9-31.3-19.1-49.4-19.1-42.9,0-77.2,35.5-77.2,78.1S142.3,334,185.3,334c32.6,0,64.9-19.1,70.1-53.3H185.3V238.1H302.2a109.2,109.2,0,0,1,1.9,20.7c0,70.8-47.5,121.2-118.8,121.2ZM415.5,273.8v35.5H380V273.8H344.5V238.3H380V202.8h35.5v35.5h35.2v35.5Z"></path></svg><small><strong>Log in</strong> with <strong>Google</strong></small></button><br /><style type="text/css">.sign-in-with-apple-button { width: 100%; height: 52px; border-radius: 3px; border: 1px solid black; cursor: pointer; }</style><script src="https://appleid.cdn-apple.com/appleauth/static/jsapi/appleid/1/en_US/appleid.auth.js" type="text/javascript"></script><div class="sign-in-with-apple-button" data-border="false" data-color="white" id="appleid-signin"><span   ="Sign Up with Apple" class="u-fs11"></span></div><script>AppleID.auth.init({ clientId: 'edu.academia.applesignon', scope: 'name email', redirectURI: 'https://www.academia.edu/sessions', state: "663d94607d3ea28d762d22a5231c05bdc943842c54574f01c89a50d39afe8c60", });</script><script>// Hacky way of checking if on fast loswp if (window.loswp == null) { (function() { const Google = window?.Aedu?.Auth?.OauthButton?.Login?.Google; const Facebook = window?.Aedu?.Auth?.OauthButton?.Login?.Facebook; if (Google) { new Google({ el: '#login-google-oauth-button', rememberMeCheckboxId: 'remember_me', track: null }); } if (Facebook) { new Facebook({ el: '#login-facebook-oauth-button', rememberMeCheckboxId: 'remember_me', track: null }); } })(); }</script></div></div></div><div class="modal-body"><div class="row"><div class="col-xs-10 col-xs-offset-1"><div class="hr-heading login-hr-heading"><span class="hr-heading-text">or</span></div></div></div></div><div class="modal-body"><div class="row"><div class="col-xs-10 col-xs-offset-1"><form class="js-login-form" action="https://www.academia.edu/sessions" accept-charset="UTF-8" method="post"><input name="utf8" type="hidden" value="✓" autocomplete="off" /><input type="hidden" name="authenticity_token" value="ZRkGewRt2grTJWQIhZvXCMnOgdYyx6ftWVcjcGUBeQCYI/3sG43OL02PfSE+3SYLu0MuX5yBe5G+lrwDKfQ5kA==" autocomplete="off" /><div class="form-group"><label class="control-label" for="login-modal-email-input" style="font-size: 14px;">Email</label><input class="form-control" id="login-modal-email-input" name="login" type="email" /></div><div class="form-group"><label class="control-label" for="login-modal-password-input" style="font-size: 14px;">Password</label><input class="form-control" id="login-modal-password-input" name="password" type="password" /></div><input type="hidden" name="post_login_redirect_url" id="post_login_redirect_url" value="https://www.academia.edu/112693131/Effects_of_ramification_and_connectivity_degree_on_site_percolation_threshold_on_regular_lattices_and_fractal_networks" autocomplete="off" /><div class="checkbox"><label><input type="checkbox" name="remember_me" id="remember_me" value="1" checked="checked" /><small style="font-size: 12px; margin-top: 2px; display: inline-block;">Remember me on this computer</small></label></div><br><input type="submit" name="commit" value="Log In" class="btn btn-primary btn-block btn-lg js-login-submit" data-disable-with="Log In" /></br></form><script>typeof window?.Aedu?.recaptchaManagedForm === 'function' && window.Aedu.recaptchaManagedForm( document.querySelector('.js-login-form'), document.querySelector('.js-login-submit') );</script><small style="font-size: 12px;"><br />or <a data-target="#login-modal-reset-password-container" data-toggle="collapse" href="javascript:void(0)">reset password</a></small><div class="collapse" id="login-modal-reset-password-container"><br /><div class="well margin-0x"><form class="js-password-reset-form" action="https://www.academia.edu/reset_password" accept-charset="UTF-8" method="post"><input name="utf8" type="hidden" value="✓" autocomplete="off" /><input type="hidden" name="authenticity_token" value="h2Zg25KWQrw7Q3LDAM3j9CSrctbUpdueDLRt+m9meLB6XJtMjXZWmaXpa+q7ixL3VibdX3rjB+LrdfKJI5M4IA==" autocomplete="off" /><p>Enter the email address you signed up with and we'll email you a reset link.</p><div class="form-group"><input class="form-control" name="email" type="email" /></div><input class="btn btn-primary btn-block g-recaptcha js-password-reset-submit" data-sitekey="6Lf3KHUUAAAAACggoMpmGJdQDtiyrjVlvGJ6BbAj" type="submit" value="Email me a link" /></form></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/collapse-45805421cf446ca5adf7aaa1935b08a3a8d1d9a6cc5d91a62a2a3a00b20b3e6a.js"], function() { // from javascript_helper.rb $("#login-modal-reset-password-container").on("shown.bs.collapse", function() { $(this).find("input[type=email]").focus(); }); }); </script> </div></div></div><div class="modal-footer"><div class="text-center"><small style="font-size: 12px;">Need an account? <a rel="nofollow" href="https://www.academia.edu/signup">Click here to sign up</a></small></div></div></div></div></div></div><script>// If we are on subdomain or non-bootstrapped page, redirect to login page instead of showing modal (function(){ if (typeof $ === 'undefined') return; var host = window.location.hostname; if ((host === $domain || host === "www."+$domain) && (typeof $().modal === 'function')) { $("#nav_log_in").click(function(e) { // Don't follow the link and open the modal e.preventDefault(); $("#login-modal").on('shown.bs.modal', function() { $(this).find("#login-modal-email-input").focus() }).modal('show'); }); } })()</script> <div id="fb-root"></div><script>window.fbAsyncInit = function() { FB.init({ appId: "2369844204", version: "v8.0", status: true, cookie: true, xfbml: true }); // Additional initialization code. if (window.InitFacebook) { // facebook.ts already loaded, set it up. window.InitFacebook(); } else { // Set a flag for facebook.ts to find when it loads. window.academiaAuthReadyFacebook = true; } };</script> <div id="google-root"></div><script>window.loadGoogle = function() { if (window.InitGoogle) { // google.ts already loaded, set it up. window.InitGoogle("331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b"); } else { // Set a flag for google.ts to use when it loads. window.GoogleClientID = "331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b"; } };</script> <div class="header--container" id="main-header-container"><div class="header--inner-container header--inner-container-ds2"><div class="header-ds2--left-wrapper"><div class="header-ds2--left-wrapper-inner"><a data-main-header-link-target="logo_home" href="https://www.academia.edu/"><img class="hide-on-desktop-redesign" style="height: 24px; width: 24px;" alt="Academia.edu" src="//a.academia-assets.com/images/academia-logo-redesign-2015-A.svg" width="24" height="24" /><img width="145.2" height="18" class="hide-on-mobile-redesign" style="height: 24px;" alt="Academia.edu" src="//a.academia-assets.com/images/academia-logo-redesign-2015.svg" /></a><div class="header--search-container header--search-container-ds2"><form class="js-SiteSearch-form select2-no-default-pills" action="https://www.academia.edu/search" accept-charset="UTF-8" method="get"><input name="utf8" type="hidden" value="✓" autocomplete="off" /><svg style="width: 14px; height: 14px;" aria-hidden="true" focusable="false" data-prefix="fas" data-icon="search" class="header--search-icon svg-inline--fa fa-search fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M505 442.7L405.3 343c-4.5-4.5-10.6-7-17-7H372c27.6-35.3 44-79.7 44-128C416 93.1 322.9 0 208 0S0 93.1 0 208s93.1 208 208 208c48.3 0 92.7-16.4 128-44v16.3c0 6.4 2.5 12.5 7 17l99.7 99.7c9.4 9.4 24.6 9.4 33.9 0l28.3-28.3c9.4-9.4 9.4-24.6.1-34zM208 336c-70.7 0-128-57.2-128-128 0-70.7 57.2-128 128-128 70.7 0 128 57.2 128 128 0 70.7-57.2 128-128 128z"></path></svg><input class="header--search-input header--search-input-ds2 js-SiteSearch-form-input" data-main-header-click-target="search_input" name="q" placeholder="Search" type="text" /></form></div></div></div><nav class="header--nav-buttons header--nav-buttons-ds2 js-main-nav"><a class="ds2-5-button ds2-5-button--secondary js-header-login-url header-button-ds2 header-login-ds2 hide-on-mobile-redesign" href="https://www.academia.edu/login" rel="nofollow">Log In</a><a class="ds2-5-button ds2-5-button--secondary header-button-ds2 hide-on-mobile-redesign" href="https://www.academia.edu/signup" rel="nofollow">Sign Up</a><button class="header--hamburger-button header--hamburger-button-ds2 hide-on-desktop-redesign js-header-hamburger-button"><div class="icon-bar"></div><div class="icon-bar" style="margin-top: 4px;"></div><div class="icon-bar" style="margin-top: 4px;"></div></button></nav></div><ul class="header--dropdown-container js-header-dropdown"><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://www.academia.edu/login" rel="nofollow">Log In</a></li><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://www.academia.edu/signup" rel="nofollow">Sign Up</a></li><li class="header--dropdown-row js-header-dropdown-expand-button"><button class="header--dropdown-button">more<svg aria-hidden="true" focusable="false" data-prefix="fas" data-icon="caret-down" class="header--dropdown-button-icon svg-inline--fa fa-caret-down fa-w-10" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 320 512"><path fill="currentColor" d="M31.3 192h257.3c17.8 0 26.7 21.5 14.1 34.1L174.1 354.8c-7.8 7.8-20.5 7.8-28.3 0L17.2 226.1C4.6 213.5 13.5 192 31.3 192z"></path></svg></button></li><li><ul class="header--expanded-dropdown-container"><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://www.academia.edu/about">About</a></li><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://www.academia.edu/press">Press</a></li><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://medium.com/@academia">Blog</a></li><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://www.academia.edu/documents">Papers</a></li><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://www.academia.edu/terms">Terms</a></li><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://www.academia.edu/privacy">Privacy</a></li><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://www.academia.edu/copyright">Copyright</a></li><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://www.academia.edu/hiring"><svg aria-hidden="true" focusable="false" data-prefix="fas" data-icon="briefcase" class="header--dropdown-row-icon svg-inline--fa fa-briefcase fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M320 336c0 8.84-7.16 16-16 16h-96c-8.84 0-16-7.16-16-16v-48H0v144c0 25.6 22.4 48 48 48h416c25.6 0 48-22.4 48-48V288H320v48zm144-208h-80V80c0-25.6-22.4-48-48-48H176c-25.6 0-48 22.4-48 48v48H48c-25.6 0-48 22.4-48 48v80h512v-80c0-25.6-22.4-48-48-48zm-144 0H192V96h128v32z"></path></svg>We're Hiring!</a></li><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://support.academia.edu/"><svg aria-hidden="true" focusable="false" data-prefix="fas" data-icon="question-circle" class="header--dropdown-row-icon svg-inline--fa fa-question-circle fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M504 256c0 136.997-111.043 248-248 248S8 392.997 8 256C8 119.083 119.043 8 256 8s248 111.083 248 248zM262.655 90c-54.497 0-89.255 22.957-116.549 63.758-3.536 5.286-2.353 12.415 2.715 16.258l34.699 26.31c5.205 3.947 12.621 3.008 16.665-2.122 17.864-22.658 30.113-35.797 57.303-35.797 20.429 0 45.698 13.148 45.698 32.958 0 14.976-12.363 22.667-32.534 33.976C247.128 238.528 216 254.941 216 296v4c0 6.627 5.373 12 12 12h56c6.627 0 12-5.373 12-12v-1.333c0-28.462 83.186-29.647 83.186-106.667 0-58.002-60.165-102-116.531-102zM256 338c-25.365 0-46 20.635-46 46 0 25.364 20.635 46 46 46s46-20.636 46-46c0-25.365-20.635-46-46-46z"></path></svg>Help Center</a></li><li class="header--dropdown-row js-header-dropdown-collapse-button"><button class="header--dropdown-button">less<svg aria-hidden="true" focusable="false" data-prefix="fas" data-icon="caret-up" class="header--dropdown-button-icon svg-inline--fa fa-caret-up fa-w-10" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 320 512"><path fill="currentColor" d="M288.662 352H31.338c-17.818 0-26.741-21.543-14.142-34.142l128.662-128.662c7.81-7.81 20.474-7.81 28.284 0l128.662 128.662c12.6 12.599 3.676 34.142-14.142 34.142z"></path></svg></button></li></ul></li></ul></div> <script src="//a.academia-assets.com/assets/webpack_bundles/fast_loswp-bundle-bf3d831cde46cd0e142f29f81a3fc4ce5ab45a404c10c12a480e83de68aff851.js" defer="defer"></script><script>window.loswp = {}; window.loswp.author = 31879133; window.loswp.bulkDownloadFilterCounts = {}; window.loswp.hasDownloadableAttachment = true; window.loswp.hasViewableAttachments = true; // TODO: just use routes for this window.loswp.loginUrl = "https://www.academia.edu/login?post_login_redirect_url=https%3A%2F%2Fwww.academia.edu%2F112693131%2FEffects_of_ramification_and_connectivity_degree_on_site_percolation_threshold_on_regular_lattices_and_fractal_networks%3Fauto%3Ddownload"; window.loswp.translateUrl = "https://www.academia.edu/login?post_login_redirect_url=https%3A%2F%2Fwww.academia.edu%2F112693131%2FEffects_of_ramification_and_connectivity_degree_on_site_percolation_threshold_on_regular_lattices_and_fractal_networks%3Fshow_translation%3Dtrue"; window.loswp.previewableAttachments = [{"id":109843796,"identifier":"Attachment_109843796","shouldShowBulkDownload":false}]; window.loswp.shouldDetectTimezone = true; window.loswp.shouldShowBulkDownload = true; window.loswp.showSignupCaptcha = false window.loswp.willEdgeCache = false; window.loswp.work = {"work":{"id":112693131,"created_at":"2023-12-31T15:42:18.794-08:00","from_world_paper_id":247215480,"updated_at":"2024-11-06T04:48:06.639-08:00","_data":{"publisher":"Elsevier BV","publication_date":"2019,3,1","publication_name":"Physics Letters"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Effects of ramification and connectivity degree on site percolation threshold on regular lattices and fractal networks","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [31879133]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "full_page_mobile_sutd_modal"; window.loswp.useOptimizedScribd4genScript = false; window.loswp.appleClientId = 'edu.academia.applesignon';</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{"location":"swp-splash-paper-cover","attachmentId":109843796,"attachmentType":"pdf"}"><img alt="First page of “Effects of ramification and connectivity degree on site percolation threshold on regular lattices and fractal networks”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/109843796/mini_magick20231231-1-doqv75.png?1704066238" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/assets/single_work_splash/adobe.icon-574afd46eb6b03a77a153a647fb47e30546f9215c0ee6a25df597a779717f9ef.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">Effects of ramification and connectivity degree on site percolation threshold on regular lattices and fractal networks</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="31879133" href="https://independent.academia.edu/AlexanderBalankin"><img alt="Profile image of Alexander Balankin" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/31879133/53408813/41535800/s65_alexander.balankin.gif" />Alexander Balankin</a></div><p class="ds-work-card--detail ds2-5-body-sm">2019, Physics Letters</p><div class="ds-work-card--button-container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--work-card","attachmentId":109843796,"attachmentType":"pdf","workUrl":"https://www.academia.edu/112693131/Effects_of_ramification_and_connectivity_degree_on_site_percolation_threshold_on_regular_lattices_and_fractal_networks"}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--work-card","attachmentId":109843796,"attachmentType":"pdf","workUrl":"https://www.academia.edu/112693131/Effects_of_ramification_and_connectivity_degree_on_site_percolation_threshold_on_regular_lattices_and_fractal_networks"}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div></div><div data-auto_select="false" data-client_id="331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b" data-doc_id="109843796" data-landing_url="https://www.academia.edu/112693131/Effects_of_ramification_and_connectivity_degree_on_site_percolation_threshold_on_regular_lattices_and_fractal_networks" data-login_uri="https://www.academia.edu/registrations/google_one_tap" data-moment_callback="onGoogleOneTapEvent" id="g_id_onload"></div><div class="ds-top-related-works--grid-container"><div class="ds-related-content--container ds-top-related-works--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="0" data-entity-id="88751162" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/88751162/Percolation_on_infinitely_ramified_fractal_networks">Percolation on infinitely ramified fractal networks</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="241020478" href="https://independent.academia.edu/OrlandoSusarreyHuerta">Orlando Susarrey Huerta</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physics Letters A, 2018</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Percolation on infinitely ramified fractal networks","attachmentId":92667243,"attachmentType":"pdf","work_url":"https://www.academia.edu/88751162/Percolation_on_infinitely_ramified_fractal_networks","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/88751162/Percolation_on_infinitely_ramified_fractal_networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="1" data-entity-id="32428505" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/32428505/Percolation_on_a_multifractal_scale_free_planar_stochastic_lattice_and_its_universality_class">Percolation on a multifractal scale-free planar stochastic lattice and its universality class</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="62710135" href="https://independent.academia.edu/kamrulHossain8">Kamrul Hassan</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review E, 2015</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Percolation on a multifractal scale-free planar stochastic lattice and its universality class","attachmentId":52622835,"attachmentType":"pdf","work_url":"https://www.academia.edu/32428505/Percolation_on_a_multifractal_scale_free_planar_stochastic_lattice_and_its_universality_class","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/32428505/Percolation_on_a_multifractal_scale_free_planar_stochastic_lattice_and_its_universality_class"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="2" data-entity-id="32428506" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/32428506/New_universality_class_in_percolation_on_multifractal_scale_free_planar_stochastic_lattice">New universality class in percolation on multifractal scale-free planar stochastic lattice</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="62710135" href="https://independent.academia.edu/kamrulHossain8">Kamrul Hassan</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"New universality class in percolation on multifractal scale-free planar stochastic lattice","attachmentId":52622852,"attachmentType":"pdf","work_url":"https://www.academia.edu/32428506/New_universality_class_in_percolation_on_multifractal_scale_free_planar_stochastic_lattice","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/32428506/New_universality_class_in_percolation_on_multifractal_scale_free_planar_stochastic_lattice"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="3" data-entity-id="8100594" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/8100594/Percolation_on_a_multifractal">Percolation on a multifractal</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="15699231" href="https://ucu.academia.edu/EliasdeFreitas">Elias de Freitas</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review E, 2004</p><p class="ds-related-work--abstract ds2-5-body-sm">We investigate percolation phenomena in multifractal objects that are built in a simple way. In these objects the multifractality comes directly from the geometric tiling. We identify some differences between percolation in the proposed multifractals and in a regular lattice. There are basically two sources of these differences. The first is related to the coordination number, which changes along the multifractal. The second comes from the way the weight of each cell in the multifractal affects the percolation cluster. We use many samples of finite size lattices and draw the histogram of percolating lattices against site occupation probability. Depending on a parameter characterizing the multifractal and the lattice size, the histogram can have two peaks. We observe that the percolation threshold for the multifractal is lower than that for the square lattice. We compute the fractal dimension of the percolating cluster and the critical exponent β. Despite the topological differences, we find that the percolation in a multifractal support is in the same universality class as standard percolation.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Percolation on a multifractal","attachmentId":48214723,"attachmentType":"pdf","work_url":"https://www.academia.edu/8100594/Percolation_on_a_multifractal","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/8100594/Percolation_on_a_multifractal"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="4" data-entity-id="61395145" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/61395145/Universal_Behavior_of_Connectivity_Properties_in_Fractal_Percolation_Models">Universal Behavior of Connectivity Properties in Fractal Percolation Models</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="52848710" href="https://independent.academia.edu/FedericoCamia">Federico Camia</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Electronic Journal of Probability, 2010</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Universal Behavior of Connectivity Properties in Fractal Percolation Models","attachmentId":74438601,"attachmentType":"pdf","work_url":"https://www.academia.edu/61395145/Universal_Behavior_of_Connectivity_Properties_in_Fractal_Percolation_Models","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/61395145/Universal_Behavior_of_Connectivity_Properties_in_Fractal_Percolation_Models"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="5" data-entity-id="16867064" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/16867064/Percolation_thresholds_on_finitely_ramified_fractals">Percolation thresholds on finitely ramified fractals</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="26329343" href="https://independent.academia.edu/PeterGrassberger">Peter Grassberger</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Physics A: Mathematical and General, 1990</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Percolation thresholds on finitely ramified fractals","attachmentId":39227019,"attachmentType":"pdf","work_url":"https://www.academia.edu/16867064/Percolation_thresholds_on_finitely_ramified_fractals","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/16867064/Percolation_thresholds_on_finitely_ramified_fractals"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="5447038" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/5447038/Beyond_Blobs_in_Percolation_Cluster_Structure_The_Distribution_of_3_Blocks_at_the_Percolation_Threshold">Beyond Blobs in Percolation Cluster Structure: The Distribution of 3-Blocks at the Percolation Threshold</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="7630487" href="https://bu.academia.edu/EugeneStanley">Eugene Stanley</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Beyond Blobs in Percolation Cluster Structure: The Distribution of 3-Blocks at the Percolation Threshold","attachmentId":32570300,"attachmentType":"pdf","work_url":"https://www.academia.edu/5447038/Beyond_Blobs_in_Percolation_Cluster_Structure_The_Distribution_of_3_Blocks_at_the_Percolation_Threshold","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/5447038/Beyond_Blobs_in_Percolation_Cluster_Structure_The_Distribution_of_3_Blocks_at_the_Percolation_Threshold"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="18237064" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/18237064/On_the_Fractal_dimension_and_correlations_in_percolation_theory">On the Fractal dimension and correlations in percolation theory</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="38221071" href="https://bgu.academia.edu/AmnonAharony">Amnon Aharony</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Statistical Physics, 1984</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On the Fractal dimension and correlations in percolation theory","attachmentId":39948825,"attachmentType":"pdf","work_url":"https://www.academia.edu/18237064/On_the_Fractal_dimension_and_correlations_in_percolation_theory","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/18237064/On_the_Fractal_dimension_and_correlations_in_percolation_theory"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="69177732" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/69177732/Fat_fractal_percolation_and_k_fractal_percolation">Fat fractal percolation and k-fractal percolation</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="52848710" href="https://independent.academia.edu/FedericoCamia">Federico Camia</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Latin American journal of probability and mathematical statistics</p><p class="ds-related-work--abstract ds2-5-body-sm">We consider two variations on the Mandelbrot fractal percolation model. In the k-fractal percolation model, the d-dimensional unit cube is divided in N^d equal subcubes, k of which are retained while the others are discarded. The procedure is then iterated inside the retained cubes at all smaller scales. We show that the (properly rescaled) percolation critical value of this model converges to the critical value of ordinary site percolation on a particular d-dimensional lattice as N tends to infinity. This is analogous to the result of Falconer and Grimmett that the critical value for Mandelbrot fractal percolation converges to the critical value of site percolation on the same d-dimensional lattice. In the fat fractal percolation model, subcubes are retained with probability p_n at step n of the construction, where (p_n) is a non-decreasing sequence with \prod p_n &gt; 0. The Lebesgue measure of the limit set is positive a.s. given non-extinction. We prove that either the set of co...</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Fat fractal percolation and k-fractal percolation","attachmentId":79372658,"attachmentType":"pdf","work_url":"https://www.academia.edu/69177732/Fat_fractal_percolation_and_k_fractal_percolation","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/69177732/Fat_fractal_percolation_and_k_fractal_percolation"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="52412909" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/52412909/Percolation_on_an_isotropically_directed_lattice">Percolation on an isotropically directed lattice</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="61311359" href="https://independent.academia.edu/AureliodeNoronha">Aurelio de Noronha</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review E</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Percolation on an isotropically directed lattice","attachmentId":69687548,"attachmentType":"pdf","work_url":"https://www.academia.edu/52412909/Percolation_on_an_isotropically_directed_lattice","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/52412909/Percolation_on_an_isotropically_directed_lattice"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":109843796,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":109843796,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_109843796" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. You can download the paper by clicking the button above.</p></div></div></div></div><div class="ds-sidebar--container js-work-sidebar"><div class="ds-related-content--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="0" data-entity-id="49182700" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/49182700/Percolation_on_infinitely_ramified_fractals">Percolation on infinitely ramified fractals</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="136645528" href="https://independent.academia.edu/DavidMovshovitz">David Movshovitz</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Statistical Physics, 1984</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Percolation on infinitely ramified fractals","attachmentId":67567229,"attachmentType":"pdf","work_url":"https://www.academia.edu/49182700/Percolation_on_infinitely_ramified_fractals","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/49182700/Percolation_on_infinitely_ramified_fractals"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="1" data-entity-id="5447810" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/5447810/The_Fractal_Dimension_of_the_Minimum_Path_in_Two_and_Three_Dimensional_Percolation">The Fractal Dimension of the Minimum Path in Two- and Three-Dimensional Percolation</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="7630487" href="https://bu.academia.edu/EugeneStanley">Eugene Stanley</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"The Fractal Dimension of the Minimum Path in Two- and Three-Dimensional Percolation","attachmentId":32571072,"attachmentType":"pdf","work_url":"https://www.academia.edu/5447810/The_Fractal_Dimension_of_the_Minimum_Path_in_Two_and_Three_Dimensional_Percolation","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/5447810/The_Fractal_Dimension_of_the_Minimum_Path_in_Two_and_Three_Dimensional_Percolation"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="2" data-entity-id="81783435" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/81783435/On_intrinsic_properties_of_fractal_lattices_and_percolation_clusters">On intrinsic properties of fractal lattices and percolation clusters</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="48874348" href="https://independent.academia.edu/JVannimenus">J. Vannimenus</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal de Physique Lettres, 1984</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On intrinsic properties of fractal lattices and percolation clusters","attachmentId":87708010,"attachmentType":"pdf","work_url":"https://www.academia.edu/81783435/On_intrinsic_properties_of_fractal_lattices_and_percolation_clusters","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/81783435/On_intrinsic_properties_of_fractal_lattices_and_percolation_clusters"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="3" data-entity-id="112693132" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/112693132/Percolation_on_Fractal_Networks_A_Survey">Percolation on Fractal Networks: A Survey</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="31879133" href="https://independent.academia.edu/AlexanderBalankin">Alexander Balankin</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Fractal and fractional, 2023</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Percolation on Fractal Networks: A Survey","attachmentId":109843759,"attachmentType":"pdf","work_url":"https://www.academia.edu/112693132/Percolation_on_Fractal_Networks_A_Survey","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/112693132/Percolation_on_Fractal_Networks_A_Survey"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="4" data-entity-id="54175838" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/54175838/Percolation_thresholds_and_Fisher_exponents_in_hypercubic_lattices">Percolation thresholds and Fisher exponents in hypercubic lattices</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="160629230" href="https://sfb-trr-62.academia.edu/StephanMertens">Stephan Mertens</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review E</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Percolation thresholds and Fisher exponents in hypercubic lattices","attachmentId":70666874,"attachmentType":"pdf","work_url":"https://www.academia.edu/54175838/Percolation_thresholds_and_Fisher_exponents_in_hypercubic_lattices","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/54175838/Percolation_thresholds_and_Fisher_exponents_in_hypercubic_lattices"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="5" data-entity-id="17152423" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/17152423/Fractal_to_Euclidean_crossover_and_scaling_for_random_walks_on_percolation_clusters_II_Three_dimensional_lattices">Fractal to Euclidean crossover and scaling for random walks on percolation clusters. II. Three-dimensional lattices</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="36744155" href="https://independent.academia.edu/PanosArgyrakis">Panos Argyrakis</a><span>, </span><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="32994550" href="https://independent.academia.edu/RaoulKopelman">Raoul Kopelman</a></div><p class="ds-related-work--metadata ds2-5-body-xs">The Journal of Chemical Physics, 1985</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Fractal to Euclidean crossover and scaling for random walks on percolation clusters. II. Three-dimensional lattices","attachmentId":42302303,"attachmentType":"pdf","work_url":"https://www.academia.edu/17152423/Fractal_to_Euclidean_crossover_and_scaling_for_random_walks_on_percolation_clusters_II_Three_dimensional_lattices","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/17152423/Fractal_to_Euclidean_crossover_and_scaling_for_random_walks_on_percolation_clusters_II_Three_dimensional_lattices"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="6" data-entity-id="20806466" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/20806466/Critical_properties_of_random_site_percolation_in_two_and_three_dimensions_A_Monte_Carlo_study">Critical properties of random-site percolation in two and three dimensions: A Monte Carlo study</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="42094488" href="https://marquette.academia.edu/MartinCorsten">Martin Corsten</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physica A: Statistical Mechanics and its Applications, 1989</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Critical properties of random-site percolation in two and three dimensions: A Monte Carlo study","attachmentId":41572756,"attachmentType":"pdf","work_url":"https://www.academia.edu/20806466/Critical_properties_of_random_site_percolation_in_two_and_three_dimensions_A_Monte_Carlo_study","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/20806466/Critical_properties_of_random_site_percolation_in_two_and_three_dimensions_A_Monte_Carlo_study"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="7" data-entity-id="97490994" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/97490994/Percolation_in_a_distorted_square_lattice">Percolation in a distorted square lattice</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="28145192" href="https://independent.academia.edu/SayantanMitra3">Sayantan Mitra</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review E, 2019</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Percolation in a distorted square lattice","attachmentId":99098050,"attachmentType":"pdf","work_url":"https://www.academia.edu/97490994/Percolation_in_a_distorted_square_lattice","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/97490994/Percolation_in_a_distorted_square_lattice"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="8" data-entity-id="75159609" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/75159609/Universal_scaling_functions_for_bond_percolation_on_planar_random_and_square_lattices_with_multiple_percolating_clusters">Universal scaling functions for bond percolation on planar random and square lattices with multiple percolating clusters</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="59280610" href="https://independent.academia.edu/SimonLin23">Simon Lin</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2001</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Universal scaling functions for bond percolation on planar random and square lattices with multiple percolating clusters","attachmentId":83041011,"attachmentType":"pdf","work_url":"https://www.academia.edu/75159609/Universal_scaling_functions_for_bond_percolation_on_planar_random_and_square_lattices_with_multiple_percolating_clusters","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/75159609/Universal_scaling_functions_for_bond_percolation_on_planar_random_and_square_lattices_with_multiple_percolating_clusters"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="9" data-entity-id="5447809" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/5447809/The_Fractal_Dimension_and_Other_Percolation_Exponents_in_Four_and_Five_Dimensions">The Fractal Dimension and Other Percolation Exponents in Four and Five Dimensions</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="7630487" href="https://bu.academia.edu/EugeneStanley">Eugene Stanley</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"The Fractal Dimension and Other Percolation Exponents in Four and Five Dimensions","attachmentId":32571071,"attachmentType":"pdf","work_url":"https://www.academia.edu/5447809/The_Fractal_Dimension_and_Other_Percolation_Exponents_in_Four_and_Five_Dimensions","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/5447809/The_Fractal_Dimension_and_Other_Percolation_Exponents_in_Four_and_Five_Dimensions"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="10" data-entity-id="16867053" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/16867053/Agglomerative_percolation_in_two_dimensions">Agglomerative percolation in two dimensions</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="26329343" href="https://independent.academia.edu/PeterGrassberger">Peter Grassberger</a></div><p class="ds-related-work--metadata ds2-5-body-xs">EPL (Europhysics Letters), 2012</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Agglomerative percolation in two dimensions","attachmentId":39227014,"attachmentType":"pdf","work_url":"https://www.academia.edu/16867053/Agglomerative_percolation_in_two_dimensions","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/16867053/Agglomerative_percolation_in_two_dimensions"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="11" data-entity-id="112439531" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/112439531/Percolation_on_branching_simplicial_and_cell_complexes_and_its_relation_to_interdependent_percolation">Percolation on branching simplicial and cell complexes and its relation to interdependent percolation</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="35256933" href="https://qmul.academia.edu/GinestraBianconi">Ginestra Bianconi</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review E, 2019</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Percolation on branching simplicial and cell complexes and its relation to interdependent percolation","attachmentId":109669808,"attachmentType":"pdf","work_url":"https://www.academia.edu/112439531/Percolation_on_branching_simplicial_and_cell_complexes_and_its_relation_to_interdependent_percolation","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/112439531/Percolation_on_branching_simplicial_and_cell_complexes_and_its_relation_to_interdependent_percolation"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="12" data-entity-id="89896103" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/89896103/Physical_Properties_of_a_New_Fractal_Model_of_Percolation_Clusters">Physical Properties of a New Fractal Model of Percolation Clusters</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="31313596" href="https://independent.academia.edu/AAharony">A. Aharony</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review Letters, 1984</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Physical Properties of a New Fractal Model of Percolation Clusters","attachmentId":93609890,"attachmentType":"pdf","work_url":"https://www.academia.edu/89896103/Physical_Properties_of_a_New_Fractal_Model_of_Percolation_Clusters","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/89896103/Physical_Properties_of_a_New_Fractal_Model_of_Percolation_Clusters"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="13" data-entity-id="48351108" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/48351108/Shortest_path_fractal_dimension_for_percolation_in_two_and_three_dimensions">Shortest-path fractal dimension for percolation in two and three dimensions</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="282899" href="https://umich.academia.edu/RobertZiff">Robert Ziff</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review E, 2012</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Shortest-path fractal dimension for percolation in two and three dimensions","attachmentId":67009732,"attachmentType":"pdf","work_url":"https://www.academia.edu/48351108/Shortest_path_fractal_dimension_for_percolation_in_two_and_three_dimensions","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/48351108/Shortest_path_fractal_dimension_for_percolation_in_two_and_three_dimensions"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="14" data-entity-id="54175841" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/54175841/Percolation_thresholds_in_hyperbolic_lattices">Percolation thresholds in hyperbolic lattices</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="160629230" href="https://sfb-trr-62.academia.edu/StephanMertens">Stephan Mertens</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review E</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Percolation thresholds in hyperbolic lattices","attachmentId":70666878,"attachmentType":"pdf","work_url":"https://www.academia.edu/54175841/Percolation_thresholds_in_hyperbolic_lattices","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/54175841/Percolation_thresholds_in_hyperbolic_lattices"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="15" data-entity-id="22106521" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/22106521/Percolation_on_two_and_three_dimensional_lattices">Percolation on two- and three-dimensional lattices</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="43414141" href="https://independent.academia.edu/JPlascak">J. Plascak</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical review. E, Statistical, nonlinear, and soft matter physics, 2003</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Percolation on two- and three-dimensional lattices","attachmentId":42775430,"attachmentType":"pdf","work_url":"https://www.academia.edu/22106521/Percolation_on_two_and_three_dimensional_lattices","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/22106521/Percolation_on_two_and_three_dimensional_lattices"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="16" data-entity-id="55156423" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/55156423/Finite_size_scaling_of_clique_percolation_on_two_dimensional_Moore_lattices">Finite-size scaling of clique percolation on two-dimensional Moore lattices</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="32185066" href="https://independent.academia.edu/ZiGangHuang">Zi-Gang Huang</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical review. E, 2018</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Finite-size scaling of clique percolation on two-dimensional Moore lattices","attachmentId":71162684,"attachmentType":"pdf","work_url":"https://www.academia.edu/55156423/Finite_size_scaling_of_clique_percolation_on_two_dimensional_Moore_lattices","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/55156423/Finite_size_scaling_of_clique_percolation_on_two_dimensional_Moore_lattices"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="17" data-entity-id="31699791" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/31699791/Self_organized_percolation_growth_in_regular_and_disordered_lattices">Self-organized percolation growth in regular and disordered lattices</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="60898253" href="https://bnfghhtrhtbnhfdhtryht.academia.edu/FranciscoCavalcante">Francisco Cavalcante</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physica A: Statistical Mechanics and its Applications, 2002</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Self-organized percolation growth in regular and disordered lattices","attachmentId":52015343,"attachmentType":"pdf","work_url":"https://www.academia.edu/31699791/Self_organized_percolation_growth_in_regular_and_disordered_lattices","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/31699791/Self_organized_percolation_growth_in_regular_and_disordered_lattices"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="18" data-entity-id="5447721" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/5447721/Site_Percolation_Threshold_for_Honeycomb_and_Square_Lattices">Site Percolation Threshold for Honeycomb and Square Lattices</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="7630487" href="https://bu.academia.edu/EugeneStanley">Eugene Stanley</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Site Percolation Threshold for Honeycomb and Square Lattices","attachmentId":32570987,"attachmentType":"pdf","work_url":"https://www.academia.edu/5447721/Site_Percolation_Threshold_for_Honeycomb_and_Square_Lattices","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/5447721/Site_Percolation_Threshold_for_Honeycomb_and_Square_Lattices"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="19" data-entity-id="27521595" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/27521595/New_percolating_structures_in_random_fractals_in_2d_and_3d">New percolating structures in random fractals in 2d and 3d</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="51612869" href="https://independent.academia.edu/MichelPerreau">Michel Perreau</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physica A: Statistical Mechanics and its Applications, 1989</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"New percolating structures in random fractals in 2d and 3d","attachmentId":47776883,"attachmentType":"pdf","work_url":"https://www.academia.edu/27521595/New_percolating_structures_in_random_fractals_in_2d_and_3d","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/27521595/New_percolating_structures_in_random_fractals_in_2d_and_3d"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="20" data-entity-id="77194604" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/77194604/Series_Expansion_of_the_Percolation_Threshold_on_Hypercubic_Lattices">Series Expansion of the Percolation Threshold on Hypercubic Lattices</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="160629230" href="https://sfb-trr-62.academia.edu/StephanMertens">Stephan Mertens</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2018</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Series Expansion of the Percolation Threshold on Hypercubic Lattices","attachmentId":84626926,"attachmentType":"pdf","work_url":"https://www.academia.edu/77194604/Series_Expansion_of_the_Percolation_Threshold_on_Hypercubic_Lattices","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/77194604/Series_Expansion_of_the_Percolation_Threshold_on_Hypercubic_Lattices"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="21" data-entity-id="16566795" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/16566795/Percolation_on_hyperbolic_lattices">Percolation on hyperbolic lattices</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="35870771" href="https://umu.academia.edu/PetterMinnhagen">Petter Minnhagen</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review E, 2009</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Percolation on hyperbolic lattices","attachmentId":42435649,"attachmentType":"pdf","work_url":"https://www.academia.edu/16566795/Percolation_on_hyperbolic_lattices","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/16566795/Percolation_on_hyperbolic_lattices"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="22" data-entity-id="13849166" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/13849166/Path_Crossing_Exponents_and_the_External_Perimeter_in_2D_Percolation">Path-Crossing Exponents and the External Perimeter in 2D Percolation</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="32943636" href="https://independent.academia.edu/BertrandDuplantier">Bertrand Duplantier</a><span>, </span><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="33005068" href="https://independent.academia.edu/MichaelAizenman">Michael Aizenman</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review Letters, 1999</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Path-Crossing Exponents and the External Perimeter in 2D Percolation","attachmentId":44882376,"attachmentType":"pdf","work_url":"https://www.academia.edu/13849166/Path_Crossing_Exponents_and_the_External_Perimeter_in_2D_Percolation","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/13849166/Path_Crossing_Exponents_and_the_External_Perimeter_in_2D_Percolation"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div><div class="ds-related-content--container"><h2 class="ds-related-content--heading">Related topics</h2><div class="ds-research-interests--pills-container"><a class="js-related-research-interest ds-research-interests--pill" data-entity-id="498" href="https://www.academia.edu/Documents/in/Physics">Physics</a><a class="js-related-research-interest ds-research-interests--pill" data-entity-id="16460" href="https://www.academia.edu/Documents/in/Statistical_Physics">Statistical Physics</a><a class="js-related-research-interest ds-research-interests--pill" data-entity-id="80414" href="https://www.academia.edu/Documents/in/Mathematical_Sciences">Mathematical Sciences</a><a class="js-related-research-interest ds-research-interests--pill" data-entity-id="118582" href="https://www.academia.edu/Documents/in/Physical_sciences">Physical sciences</a><a class="js-related-research-interest ds-research-interests--pill" data-entity-id="172625" href="https://www.academia.edu/Documents/in/Fractal">Fractal</a><a class="js-related-research-interest ds-research-interests--pill" data-entity-id="385916" href="https://www.academia.edu/Documents/in/Percolation_threshold">Percolation threshold</a><a class="js-related-research-interest ds-research-interests--pill" data-entity-id="1233815" href="https://www.academia.edu/Documents/in/Percolation_Theory">Percolation Theory</a><a class="js-related-research-interest ds-research-interests--pill" data-entity-id="1713495" href="https://www.academia.edu/Documents/in/Degree_in_music">Degree in music</a><a class="js-related-research-interest ds-research-interests--pill" data-entity-id="3591712" href="https://www.academia.edu/Documents/in/Physics_Letters_A">Physics Letters A</a></div></div></div></div></div><div class="footer--content"><ul class="footer--main-links hide-on-mobile"><li><a href="https://www.academia.edu/about">About</a></li><li><a href="https://www.academia.edu/press">Press</a></li><li><a rel="nofollow" href="https://medium.com/academia">Blog</a></li><li><a href="https://www.academia.edu/documents">Papers</a></li><li><a href="https://www.academia.edu/topics">Topics</a></li><li><a href="https://www.academia.edu/hiring"><svg style="width: 13px; height: 13px; position: relative; bottom: -1px;" aria-hidden="true" focusable="false" data-prefix="fas" data-icon="briefcase" class="svg-inline--fa fa-briefcase fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M320 336c0 8.84-7.16 16-16 16h-96c-8.84 0-16-7.16-16-16v-48H0v144c0 25.6 22.4 48 48 48h416c25.6 0 48-22.4 48-48V288H320v48zm144-208h-80V80c0-25.6-22.4-48-48-48H176c-25.6 0-48 22.4-48 48v48H48c-25.6 0-48 22.4-48 48v80h512v-80c0-25.6-22.4-48-48-48zm-144 0H192V96h128v32z"></path></svg> <strong>We're Hiring!</strong></a></li><li><a href="https://support.academia.edu/"><svg style="width: 12px; height: 12px; position: relative; bottom: -1px;" aria-hidden="true" focusable="false" data-prefix="fas" data-icon="question-circle" class="svg-inline--fa fa-question-circle fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M504 256c0 136.997-111.043 248-248 248S8 392.997 8 256C8 119.083 119.043 8 256 8s248 111.083 248 248zM262.655 90c-54.497 0-89.255 22.957-116.549 63.758-3.536 5.286-2.353 12.415 2.715 16.258l34.699 26.31c5.205 3.947 12.621 3.008 16.665-2.122 17.864-22.658 30.113-35.797 57.303-35.797 20.429 0 45.698 13.148 45.698 32.958 0 14.976-12.363 22.667-32.534 33.976C247.128 238.528 216 254.941 216 296v4c0 6.627 5.373 12 12 12h56c6.627 0 12-5.373 12-12v-1.333c0-28.462 83.186-29.647 83.186-106.667 0-58.002-60.165-102-116.531-102zM256 338c-25.365 0-46 20.635-46 46 0 25.364 20.635 46 46 46s46-20.636 46-46c0-25.365-20.635-46-46-46z"></path></svg> <strong>Help Center</strong></a></li></ul><ul class="footer--research-interests"><li>Find new research papers in:</li><li><a href="https://www.academia.edu/Documents/in/Physics">Physics</a></li><li><a href="https://www.academia.edu/Documents/in/Chemistry">Chemistry</a></li><li><a href="https://www.academia.edu/Documents/in/Biology">Biology</a></li><li><a href="https://www.academia.edu/Documents/in/Health_Sciences">Health Sciences</a></li><li><a href="https://www.academia.edu/Documents/in/Ecology">Ecology</a></li><li><a href="https://www.academia.edu/Documents/in/Earth_Sciences">Earth Sciences</a></li><li><a href="https://www.academia.edu/Documents/in/Cognitive_Science">Cognitive Science</a></li><li><a href="https://www.academia.edu/Documents/in/Mathematics">Mathematics</a></li><li><a href="https://www.academia.edu/Documents/in/Computer_Science">Computer Science</a></li></ul><ul class="footer--legal-links hide-on-mobile"><li><a href="https://www.academia.edu/terms">Terms</a></li><li><a href="https://www.academia.edu/privacy">Privacy</a></li><li><a href="https://www.academia.edu/copyright">Copyright</a></li><li>Academia ©2024</li></ul></div> </body> </html>