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Ising spins" /> <meta property="og:image" content="http://a.academia-assets.com/images/open-graph-icons/fb-paper.gif" /> <meta property="og:description" content="We investigate what happens to the third order ferromagnetic phase transition displayed by the Ising model on various dynamical planar lattices (ie coupled to 2D quantum gravity) when we introduce annealed bond disorder in the form of either" /> <meta property="article:author" content="https://hw.academia.edu/DJohnston" /> <meta name="description" content="We investigate what happens to the third order ferromagnetic phase transition displayed by the Ising model on various dynamical planar lattices (ie coupled to 2D quantum gravity) when we introduce annealed bond disorder in the form of either" /> <title>(PDF) Disorder Effects on Dynamical Ising Spins</title> <link rel="canonical" href="https://www.academia.edu/32867594/Frustrating_and_diluting_dynamical_lattice_Ising_spins" /> <script async 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{"work":{"id":32867594,"created_at":"2017-05-05T12:35:24.110-07:00","from_world_paper_id":162129963,"updated_at":"2025-02-02T23:49:55.962-08:00","_data":{"ai_title_tag":"Disorder Effects on Dynamical Ising Spins","grobid_abstract":"We investigate what happens to the third order ferromagnetic phase transition displayed by the Ising model on various dynamical planar lattices (ie coupled to 2D quantum gravity) when we introduce annealed bond disorder in the form of either antiferromagnetic couplings or null couplings. We also look at the effect of such disordering for the Ising model on general φ 3 and φ 4 Feynman diagrams.","publication_date":"1994,,","publication_name":"Physics Letters B","grobid_abstract_attachment_id":"53013041"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Frustrating and diluting dynamical lattice Ising spins","broadcastable":false,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [23419258]; 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.loginModal = {}; window.loginModal.appleClientId = 'edu.academia.applesignon'; window.userInChina = "false";</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":53013041,"attachmentType":"pdf"}"><img alt="First page of “Frustrating and diluting dynamical lattice Ising spins”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/53013041/mini_magick20190122-29499-1rskcor.png?1548162770" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/images/single_work_splash/adobe_icon.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">Frustrating and diluting dynamical lattice Ising spins</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="23419258" href="https://hw.academia.edu/DJohnston"><img alt="Profile image of Des Johnston" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/23419258/6352863/17773062/s65_des.johnston.png" />Des Johnston</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">1994, Physics Letters B</p><div class="ds-work-card--work-metadata"><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">visibility</span><p class="ds2-5-body-sm" id="work-metadata-view-count">…</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">description</span><p class="ds2-5-body-sm">7 pages</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">link</span><p class="ds2-5-body-sm">1 file</p></div></div><script>(async () => { const workId = 32867594; const worksViewsPath = "/v0/works/views?subdomain_param=api&work_ids%5B%5D=32867594"; const getWorkViews = async (workId) => { const response = await fetch(worksViewsPath); if (!response.ok) { throw new Error('Failed to load work views'); } const data = await response.json(); return data.views[workId]; }; // Get the view count for the work - we send this immediately rather than waiting for // the DOM to load, so it can be available as soon as possible (but without holding up // the backend or other resource requests, because it's a bit expensive and not critical). const viewCount = await getWorkViews(workId); const updateViewCount = (viewCount) => { try { const viewCountNumber = parseInt(viewCount, 10); if (viewCountNumber === 0) { // Remove the whole views element if there are zero views. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); return; } const commaizedViewCount = viewCountNumber.toLocaleString(); const viewCountBody = document.getElementById('work-metadata-view-count'); if (!viewCountBody) { throw new Error('Failed to find work views element'); } viewCountBody.textContent = `${commaizedViewCount} views`; } catch (error) { // Remove the whole views element if there was some issue parsing. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); throw new Error(`Failed to parse view count: ${viewCount}`, error); } }; // If the DOM is still loading, wait for it to be ready before updating the view count. if (document.readyState === "loading") { document.addEventListener('DOMContentLoaded', () => { updateViewCount(viewCount); }); // Otherwise, just update it immediately. } else { updateViewCount(viewCount); } })();</script></div><p class="ds-work-card--work-abstract ds-work-card--detail ds2-5-body-md">We investigate what happens to the third order ferromagnetic phase transition displayed by the Ising model on various dynamical planar lattices (ie coupled to 2D quantum gravity) when we introduce annealed bond disorder in the form of either antiferromagnetic couplings or null couplings. We also look at the effect of such disordering for the Ising model on general φ 3 and φ 4 Feynman diagrams.</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":53013041,"attachmentType":"pdf","workUrl":"https://www.academia.edu/32867594/Frustrating_and_diluting_dynamical_lattice_Ising_spins"}">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":53013041,"attachmentType":"pdf","workUrl":"https://www.academia.edu/32867594/Frustrating_and_diluting_dynamical_lattice_Ising_spins"}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div><div class="ds-signup-banner-trigger-container"><div class="ds-signup-banner-trigger ds-signup-banner-trigger-control"></div></div><div class="ds-signup-banner ds-signup-banner-control"><div id="ds-signup-banner-close-button"><button class="ds2-5-button ds2-5-button--secondary ds2-5-button--inverse"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">close</span></button></div><div class="ds-signup-banner-ctas"><img src="//a.academia-assets.com/images/academia-logo-capital-white.svg" /><h4 class="ds2-5-heading-serif-sm">Sign up for access to the world's latest research</h4><button class="ds2-5-button ds2-5-button--inverse ds2-5-button--full-width js-swp-download-button" data-signup-modal="{"location":"signup-banner"}">Sign up for free<span class="material-symbols-outlined" style="font-size: 20px" translate="no">arrow_forward</span></button></div><div class="ds-signup-banner-divider"></div><div class="ds-signup-banner-reasons"><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Get notified about relevant papers</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Save papers to use in your research</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Join the discussion with peers</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Track your impact</span></div></div></div><script>(() => { // Set up signup banner show/hide behavior: // 1. 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It has remarkable symmetry properties and the ground state shows topological degeneracy. The implementation of the quantum compass model in quantum simulation setups like ultracold atoms and trapped ions is far from trivial, since spin interactions in those sytems typically are independent of the spatial direction. Ising spin interactions, on the contrary, can be induced and controlled in atomic setups with state-of-the art experimental techniques. In this work, we show how the quantum compass model on a rectangular lattice can be simulated by the use of the photon-assisted tunneling induced by periodic drivings on a quantum Ising spin model. We describe a procedure to adiabatically prepare one of the doubly-degenerate ground states of this model by adiabatically ramping down a transverse magnetic field, with surprising differences depending on the parity of the lattice size. Exact diagonalizations confirm the validity of this approach for small lattices. Specific implementations of this scheme are presented with ultracold atoms in optical lattices in the Mott insulator regime, as well as with Rydberg atoms.</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":"Topological phases of shaken quantum Ising lattices","attachmentId":113740638,"attachmentType":"pdf","work_url":"https://www.academia.edu/118017266/Topological_phases_of_shaken_quantum_Ising_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-wsj-grid-card-view-pdf" href="https://www.academia.edu/118017266/Topological_phases_of_shaken_quantum_Ising_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-wsj-grid-card" data-collection-position="2" data-entity-id="32867602" 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/32867602/Ising_anti_ferromagnet_on_dynamical_triangulations_and_quadrangulations">Ising (anti-) ferromagnet on dynamical triangulations and quadrangulations</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="23419258" href="https://hw.academia.edu/DJohnston">Des Johnston</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physics Letters B, 1993</p><p class="ds-related-work--abstract ds2-5-body-sm">We write down matrix models for Ising spins with zero external field on the vertices of dynamical triangulated random surfaces (DTRS) and dynamically quadrangulated random surfaces (DQRS) and compare these with the standard matrix model approach which places the spins on the dual φ 3 and φ 4 graphs. We show that the critical temperatures calculated in the DTRS and DQRS models agree with those deduced from duality arguments in the standard approach. Using the DQRS model we observe that the Ising antiferromagnet still undergoes a phase transition to a Neel (checkerboard) ordered ground state which is absent because of frustration in the other cases.</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":"Ising (anti-) ferromagnet on dynamical triangulations and quadrangulations","attachmentId":53013038,"attachmentType":"pdf","work_url":"https://www.academia.edu/32867602/Ising_anti_ferromagnet_on_dynamical_triangulations_and_quadrangulations","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/32867602/Ising_anti_ferromagnet_on_dynamical_triangulations_and_quadrangulations"><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="114853103" 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/114853103/Unconventional_spin_frustration_due_to_two_competing_ferromagnetic_interactions_of_a_spin_1_2_Ising_Heisenberg_model_on_martini_and_martini_diced_lattice">Unconventional spin frustration due to two competing ferromagnetic interactions of a spin-1/2 Ising-Heisenberg model on martini and martini-diced 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="283577552" href="https://independent.academia.edu/JozefStrecka">Jozef Strecka</a></div><p class="ds-related-work--metadata ds2-5-body-xs">arXiv (Cornell University), 2022</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":"Unconventional spin frustration due to two competing ferromagnetic interactions of a spin-1/2 Ising-Heisenberg model on martini and martini-diced lattice","attachmentId":111432411,"attachmentType":"pdf","work_url":"https://www.academia.edu/114853103/Unconventional_spin_frustration_due_to_two_competing_ferromagnetic_interactions_of_a_spin_1_2_Ising_Heisenberg_model_on_martini_and_martini_diced_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/114853103/Unconventional_spin_frustration_due_to_two_competing_ferromagnetic_interactions_of_a_spin_1_2_Ising_Heisenberg_model_on_martini_and_martini_diced_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="4" data-entity-id="114853104" 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/114853104/Phase_diagrams_of_the_spin_1_2_Ising_Heisenberg_model_on_a_triangle_hexagon_lattice">Phase diagrams of the spin-1/2 Ising-Heisenberg model on a triangle-hexagon 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="283577552" href="https://independent.academia.edu/JozefStrecka">Jozef Strecka</a></div><p class="ds-related-work--metadata ds2-5-body-xs">arXiv (Cornell University), 2010</p><p class="ds-related-work--abstract ds2-5-body-sm">Ground-state and finite-temperature phase diagrams of a geometrically frustrated spin-1/2 Ising-Heisenberg model on a triangle-hexagon lattice are investigated within the generalized star-triangle mapping transformation. It is shown that the ground state is constituted by two different spontaneously long-range ordered phases and one disordered spin-liquid phase.</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":"Phase diagrams of the spin-1/2 Ising-Heisenberg model on a triangle-hexagon lattice","attachmentId":111432402,"attachmentType":"pdf","work_url":"https://www.academia.edu/114853104/Phase_diagrams_of_the_spin_1_2_Ising_Heisenberg_model_on_a_triangle_hexagon_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/114853104/Phase_diagrams_of_the_spin_1_2_Ising_Heisenberg_model_on_a_triangle_hexagon_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="5" data-entity-id="116289120" 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/116289120/Phase_transitions_in_the_frustrated_Ising_model_on_the_square_lattice">Phase transitions in the frustrated Ising model on the square 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="56307143" href="https://independent.academia.edu/%E6%96%87%E5%AE%89%E9%83%AD">文安郭</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review B, 2013</p><p class="ds-related-work--abstract ds2-5-body-sm">We consider the thermal phase transition from a paramagnetic to stripe-antiferromagnetic phase in the frustrated two-dimensional square-lattice Ising model with competing interactions J1 < 0 (nearest neighbor, ferromagnetic) and J2 > 0 (second neighbor, antiferromagnetic). The striped phase breaks a Z4 symmetry and is stabilized at low temperatures for g = J2/|J1| > 1/2. Despite the simplicity of the model, it has proved difficult to precisely determine the order and the universality class of the phase transitions. This was done convincingly only recently by Jin et al. [PRL 108, 045702 (2012)]. Here, we further elucidate the nature of these transitions and their anomalies by employing a combination of cluster mean-field theory, Monte Carlo simulations, and transfer-matrix calculations. The J1-J2 model has a line of very weak first-order phase transitions in the whole region 1/2 < g < g * , where g * = 0.67 ± 0.01. Thereafter, the transitions from g = g * to g → ∞ are continuous and can be fully mapped, using universality arguments, to the critical line of the well known Ashkin-Teller model from its 4-state Potts point to the decoupled Ising limit. We also comment on the pseudo-first-order behavior at the Potts point and its neighborhood in the Ashkin-Teller model on finite lattices, which in turn leads to the appearance of similar effects in the vicinity of the multicritical point g * in the J1-J2 model. The continuous transitions near g * can therefore be mistaken to be first-order transitions, and this realization was the key to understanding the paramagnetic-striped transition for the full range of g > 1/2. Most of our results are based on Monte Carlo calculations, while the cluster mean-field and transfer-matrix results provide useful methodological benchmarks for weakly first-order behaviors and Ashkin-Teller criticality.</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":"Phase transitions in the frustrated Ising model on the square lattice","attachmentId":112462067,"attachmentType":"pdf","work_url":"https://www.academia.edu/116289120/Phase_transitions_in_the_frustrated_Ising_model_on_the_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-wsj-grid-card-view-pdf" href="https://www.academia.edu/116289120/Phase_transitions_in_the_frustrated_Ising_model_on_the_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-wsj-grid-card" data-collection-position="6" data-entity-id="51227834" 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/51227834/Analysis_of_the_phase_transition_for_the_Ising_model_on_the_frustrated_square_lattice">Analysis of the phase transition for the Ising model on the frustrated square 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="167473023" href="https://cyu-fr.academia.edu/AndreasHonecker">Andreas Honecker</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review B, 2011</p><p class="ds-related-work--abstract ds2-5-body-sm">We analyze the phase transition of the frustrated J1-J2 Ising model with antiferromagnetic nearestand strong next-nearest neighbor interactions on the square lattice. Using extensive Monte Carlo simulations we show that the nature of the phase transition for 1/2 < J2/J1 1 is not of the weakly universal type-as commonly believed-but we conclude from the clearly doubly peaked structure of the energy histograms that the transition is of weak first order. Motivated by these results, we analyze the phase transitions via field-theoretic methods; i.e., we calculate the central charge of the underlying field theory via transfer-matrix techniques and present, furthermore, a field-theoretic discussion on the phase-transition behavior of the model. Starting from the conformally invariant fixed point of two decoupled critical Ising models (J1 = 0), we calculate the effect of the nearest neighbor coupling term perturbatively using operator product expansions. As an effective action we obtain the Ashkin-Teller model.</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":"Analysis of the phase transition for the Ising model on the frustrated square lattice","attachmentId":69039003,"attachmentType":"pdf","work_url":"https://www.academia.edu/51227834/Analysis_of_the_phase_transition_for_the_Ising_model_on_the_frustrated_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-wsj-grid-card-view-pdf" href="https://www.academia.edu/51227834/Analysis_of_the_phase_transition_for_the_Ising_model_on_the_frustrated_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-wsj-grid-card" data-collection-position="7" data-entity-id="74365372" 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/74365372/Absence_of_a_spontaneous_long_range_order_in_a_mixed_spin_1_2_3_2_Ising_model_on_a_decorated_square_lattice_due_to_anomalous_spin_frustration_driven_by_a_magnetoelastic_coupling">Absence of a spontaneous long-range order in a mixed spin-(1/2, 3/2) Ising model on a decorated square lattice due to anomalous spin frustration driven by a magnetoelastic coupling</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="38763024" href="https://ufla.academia.edu/OnofreRojas">Onofre Rojas</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physics Letters A</p><p class="ds-related-work--abstract ds2-5-body-sm">The mixed spin-(1/2, 3/2) Ising model on a decorated square lattice, which takes into account lattice vibrations of the spin-3/2 decorating magnetic ions at a quantum-mechanical level under the assumption of a perfect lattice rigidity of the spin-1/2 nodal magnetic ions, is examined via an exact mapping correspondence with the effective spin-1/2 Ising model on a square lattice. Although the considered magnetic structure is in principle unfrustrated due to bipartite nature of a decorated square lattice, the model under investigation may display anomalous spin frustration driven by a magnetoelastic coupling. It turns out that the magnetoelastic coupling is a primary cause for existence of the frustrated antiferromagnetic phases, which exhibit a peculiar coexistence of antiferromagnetic long-range order of the nodal spins with a partial disorder of the decorating spins with possible reentrant critical behaviour. Under certain conditions, the anomalous spin frustration caused by the magnetoelastic coupling is responsible for unprecedented absence of spontaneous long-range order in the mixed-spin Ising model composed from half-odd-integer spins only.</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":"Absence of a spontaneous long-range order in a mixed spin-(1/2, 3/2) Ising model on a decorated square lattice due to anomalous spin frustration driven by a magnetoelastic coupling","attachmentId":82544385,"attachmentType":"pdf","work_url":"https://www.academia.edu/74365372/Absence_of_a_spontaneous_long_range_order_in_a_mixed_spin_1_2_3_2_Ising_model_on_a_decorated_square_lattice_due_to_anomalous_spin_frustration_driven_by_a_magnetoelastic_coupling","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/74365372/Absence_of_a_spontaneous_long_range_order_in_a_mixed_spin_1_2_3_2_Ising_model_on_a_decorated_square_lattice_due_to_anomalous_spin_frustration_driven_by_a_magnetoelastic_coupling"><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="13508689" 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/13508689/Ising_Transition_Driven_by_Frustration_in_a_2D_Classical_Model_with_Continuous_Symmetry">Ising Transition Driven by Frustration in a 2D Classical Model with Continuous Symmetry</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="32708712" href="https://independent.academia.edu/CedricWeber">Cedric Weber</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review Letters, 2003</p><p class="ds-related-work--abstract ds2-5-body-sm">We study the thermal properties of the classical antiferromagnetic Heisenberg model with both nearest (J 1 ) and next-nearest (J 2 ) exchange couplings on the square lattice by extensive Monte Carlo simulations. We show that, for J 2 =J 1 > 1=2, thermal fluctuations give rise to an effective Z 2 symmetry leading to a finite-temperature phase transition. We provide strong numerical evidence that this transition is in the 2D Ising universality class, and that T c ! 0 with an infinite slope when J 2 =J 1 ! 1=2.</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":"Ising Transition Driven by Frustration in a 2D Classical Model with Continuous Symmetry","attachmentId":45257409,"attachmentType":"pdf","work_url":"https://www.academia.edu/13508689/Ising_Transition_Driven_by_Frustration_in_a_2D_Classical_Model_with_Continuous_Symmetry","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/13508689/Ising_Transition_Driven_by_Frustration_in_a_2D_Classical_Model_with_Continuous_Symmetry"><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="114852904" 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/114852904/Phase_transitions_of_the_mixed_spin_1_2_and_spin_Ising_model_on_a_three_dimensional_decorated_lattice_with_a_layered_structure">Phase transitions of the mixed spin-1/2 and spin- Ising model on a three-dimensional decorated lattice with a layered structure</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="283577552" href="https://independent.academia.edu/JozefStrecka">Jozef Strecka</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physica A: Statistical Mechanics and its Applications, 2009</p><p class="ds-related-work--abstract ds2-5-body-sm">Phase transitions of the mixed spin-1/2 and spinS (S ≥ 1/2) Ising model on a three-dimensional (3D) decorated lattice with a layered magnetic structure are investigated within the framework of a precise mapping relationship to the simple spin-1/2 Ising model on the tetragonal lattice. This mapping correspondence yields for the layered Ising model of mixed spins plausible results either by adopting the conjectured solution for the spin-1/2 Ising model on the orthorhombic lattice [Z.-D. Zhang, Philos. Mag. 87 (2007) 5309-5419] or by performing extensive Monte Carlo simulations for the corresponding spin-1/2 Ising model on the tetragonal lattice. It is shown that the critical behaviour markedly depends on a relative strength of axial zero-field splitting parameter, inter-and intra-layer interactions. The striking spontaneous order captured to the 'quasi-1D' spin system is found in a restricted region of interaction parameters, where the zero-field splitting parameter forces all integer-valued decorating spins towards their 'non-magnetic' spin state.</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":"Phase transitions of the mixed spin-1/2 and spin- Ising model on a three-dimensional decorated lattice with a layered structure","attachmentId":111432610,"attachmentType":"pdf","work_url":"https://www.academia.edu/114852904/Phase_transitions_of_the_mixed_spin_1_2_and_spin_Ising_model_on_a_three_dimensional_decorated_lattice_with_a_layered_structure","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/114852904/Phase_transitions_of_the_mixed_spin_1_2_and_spin_Ising_model_on_a_three_dimensional_decorated_lattice_with_a_layered_structure"><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":53013041,"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":53013041,"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_53013041" 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="31806762" 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/31806762/Spontaneous_distortion_in_the_spin_1_2_Ising_Heisenberg_model_on_decorated_planar_lattices_with_a_magnetoelastic_coupling">Spontaneous distortion in the spin-1/2 Ising-Heisenberg model on decorated planar lattices with a magnetoelastic coupling</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="38763024" href="https://ufla.academia.edu/OnofreRojas">Onofre Rojas</a></div><p class="ds-related-work--metadata ds2-5-body-xs">The European Physical Journal B, 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":"Spontaneous distortion in the spin-1/2 Ising-Heisenberg model on decorated planar lattices with a magnetoelastic coupling","attachmentId":52105015,"attachmentType":"pdf","work_url":"https://www.academia.edu/31806762/Spontaneous_distortion_in_the_spin_1_2_Ising_Heisenberg_model_on_decorated_planar_lattices_with_a_magnetoelastic_coupling","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/31806762/Spontaneous_distortion_in_the_spin_1_2_Ising_Heisenberg_model_on_decorated_planar_lattices_with_a_magnetoelastic_coupling"><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="74365371" 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/74365371/Anomalous_spin_frustration_enforced_by_a_magnetoelastic_coupling_in_the_mixed_spin_Ising_model_on_decorated_planar_lattices">Anomalous spin frustration enforced by a magnetoelastic coupling in the mixed-spin Ising model on decorated planar lattices</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" 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data-author-id="283577552" href="https://independent.academia.edu/JozefStrecka">Jozef Strecka</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Acta Physica Polonica A, 2017</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":"Spontaneous Magnetization and Phase Diagrams of the Mixed Spin-1/2 and Spin-S Ising Model on the Bethe Lattice","attachmentId":111432521,"attachmentType":"pdf","work_url":"https://www.academia.edu/114853180/Spontaneous_Magnetization_and_Phase_Diagrams_of_the_Mixed_Spin_1_2_and_Spin_S_Ising_Model_on_the_Bethe_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/114853180/Spontaneous_Magnetization_and_Phase_Diagrams_of_the_Mixed_Spin_1_2_and_Spin_S_Ising_Model_on_the_Bethe_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="3" data-entity-id="53649176" 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/53649176/The_ground_state_phase_diagrams_of_the_spin_3_2_Ising_model">The ground-state phase diagrams of the spin-3/2 Ising model</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="137790630" href="https://independent.academia.edu/MustafaKeskin57">Mustafa Keskin</a></div><p class="ds-related-work--metadata 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Correlations on the Phase Transition in an Ising Lattice","attachmentId":45218805,"attachmentType":"pdf","work_url":"https://www.academia.edu/24897553/Influence_of_the_Pair_Correlations_on_the_Phase_Transition_in_an_Ising_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/24897553/Influence_of_the_Pair_Correlations_on_the_Phase_Transition_in_an_Ising_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="5" data-entity-id="114852873" data-sort-order="default"><a class="ds-related-work--title 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href="https://up.academia.edu/OzBonfim">Oz Bonfim</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review B, 2006</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":"Quantum phase transitions in the transverse one-dimensional Ising model with four-spin interactions","attachmentId":41518691,"attachmentType":"pdf","work_url":"https://www.academia.edu/20709753/Quantum_phase_transitions_in_the_transverse_one_dimensional_Ising_model_with_four_spin_interactions","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" 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href="https://ufrgs.academia.edu/FelipeDoria">Felipe Doria</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Magnetism and Magnetic Materials, 2014</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":"Band-filling driven crossover from ferro to antiferromagnetic order in Ising lattices decorated by quantum dimers","attachmentId":84968695,"attachmentType":"pdf","work_url":"https://www.academia.edu/77658332/Band_filling_driven_crossover_from_ferro_to_antiferromagnetic_order_in_Ising_lattices_decorated_by_quantum_dimers","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" 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Ricci-tersenghi</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Physics A: Mathematical and General, 2000</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":"Coupled Ising models with disorder","attachmentId":86886337,"attachmentType":"pdf","work_url":"https://www.academia.edu/80538100/Coupled_Ising_models_with_disorder","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/80538100/Coupled_Ising_models_with_disorder"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" 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