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{"work":{"id":89819785,"created_at":"2022-11-02T14:19:37.152-07:00","from_world_paper_id":219119091,"updated_at":"2024-11-23T23:16:57.168-08:00","_data":{"grobid_abstract":"Recent theoretical results for the two-dimensional Ising model with random bonds are applied to dilute and mixed magnetic systems, The rounding effect on the quenched specific heat peak, observed in experiments with strong disorder, is explained by the the appearance of a new thermodynamic phase between the ferro-and paramagnetic phase. The relations of this result with computer simulations are discussed. In particular, finite-size effects on the disorder-induced phase are estimated.","publication_date":"1991,,","publication_name":"Journal of Magnetism and Magnetic Materials","grobid_abstract_attachment_id":"93554212"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Disordered magnetic systems in two dimensions","broadcastable":false,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [41015418]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "control"; 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":93554212,"attachmentType":"pdf"}"><img alt="First page of “Disordered magnetic systems in two dimensions”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/93554212/mini_magick20221102-1-1d7g8hw.png?1667424085" /><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">Disordered magnetic systems in two dimensions</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="41015418" href="https://uni-augsburg.academia.edu/KZiegler"><img alt="Profile image of K. Ziegler" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/41015418/11143319/12435348/s65_k..ziegler.jpg" />K. Ziegler</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">1991, Journal of Magnetism and Magnetic Materials</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">5 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 = 89819785; const worksViewsPath = "/v0/works/views?subdomain_param=api&work_ids%5B%5D=89819785"; 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">Recent theoretical results for the two-dimensional Ising model with random bonds are applied to dilute and mixed magnetic systems, The rounding effect on the quenched specific heat peak, observed in experiments with strong disorder, is explained by the the appearance of a new thermodynamic phase between the ferro-and paramagnetic phase. The relations of this result with computer simulations are discussed. 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In these dimensions, the leading exponent α, which characterizes the specific-heat critical behaviour, vanishes and no Harris prediction for the consequences of quenched disorder can be made. In the two-dimensional case, the controversy is between the strong universality hypothesis which maintains that the leading critical exponents are the same as in the pure case and the weak universality hypothesis, which favours dilution-dependent leading critical exponents. Here the random-site version of the model is subject to a finite-size scaling analysis, paying special attention to the implications for multiplicative logarithmic corrections. The analysis is fully supportive of the scaling relations for logarithmic corrections and of the strong scaling hypothesis in the 2D case. In the four-dimensional case unusual corrections to scaling characterize the model, and the precise nature of these corrections has been debated. Progress made in determining the correct 4D scenario is outlined.</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":"The quenched-disordered Ising model in two and four dimensions","attachmentId":79100086,"attachmentType":"pdf","work_url":"https://www.academia.edu/68722091/The_quenched_disordered_Ising_model_in_two_and_four_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-wsj-grid-card-view-pdf" href="https://www.academia.edu/68722091/The_quenched_disordered_Ising_model_in_two_and_four_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-wsj-grid-card" data-collection-position="2" data-entity-id="119891864" 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/119891864/Model_studies_of_the_thermal_and_magnetic_properties_in_disordered_systems">Model studies of the thermal and magnetic properties in disordered systems</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="213590493" href="https://independent.academia.edu/JavierTejada22">Javier Tejada</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Magnetism and Magnetic Materials, 1986</p><p class="ds-related-work--abstract ds2-5-body-sm">Ismg models uaith quenched disorder have been studied. both by mean-field theory and Monte Carlo methods. The disorder IS produced either ky, a magnetic field capable of values + 7j.-7; and 0. the value at each site given at random. or by non-magnetic impurltles randomly distributed through the lattice sites.</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":"Model studies of the thermal and magnetic properties in disordered systems","attachmentId":115205243,"attachmentType":"pdf","work_url":"https://www.academia.edu/119891864/Model_studies_of_the_thermal_and_magnetic_properties_in_disordered_systems","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/119891864/Model_studies_of_the_thermal_and_magnetic_properties_in_disordered_systems"><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="2491202" 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/2491202/Relaxation_to_equilibrium_for_two_dimensional_disordered_Ising_systems_in_the_Griffiths_phase">Relaxation to equilibrium for two dimensional disordered Ising systems in the Griffiths phase</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="2061400" href="https://kuleuven.academia.edu/christianmaes">christian maes</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Communications in Mathematical Physics, 1997</p><p class="ds-related-work--abstract ds2-5-body-sm">We consider Glauber-type dynamics for two dimensional disordered magnets of Ising type. We prove that, if the disorder-averaged influence of the boundary condition is sufficiently small in the equilibrium system, then the corresponding Glauber dynamics is ergodic with probability one and the disorder-average C(t) of time-autocorrelation function satisfies C(t) e −m(log t) 2 (for large t). For the standard two dimensional dilute Ising ferromagnet with i.i.d. random nearest neighbor couplings taking the values 0 or J 0 > 0, our results apply even if the active bonds percolate and J 0 is larger than the critical value J c of the corresponding pure Ising model. For the same model we also prove that in the whole Griffiths' phase the previous upper bound is optimal. This implies the existence of a dynamical phase transition which occurs when J crosses J c .</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":"Relaxation to equilibrium for two dimensional disordered Ising systems in the Griffiths phase","attachmentId":30511161,"attachmentType":"pdf","work_url":"https://www.academia.edu/2491202/Relaxation_to_equilibrium_for_two_dimensional_disordered_Ising_systems_in_the_Griffiths_phase","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/2491202/Relaxation_to_equilibrium_for_two_dimensional_disordered_Ising_systems_in_the_Griffiths_phase"><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="48600954" 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/48600954/Self_averaging_in_the_random_two_dimensional_Ising_ferromagnet">Self-averaging in the random two-dimensional Ising ferromagnet</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="3474085" href="https://nas.academia.edu/MaxymDudka">Maxym Dudka</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review E</p><p class="ds-related-work--abstract ds2-5-body-sm">We study sample-to-sample fluctuations in a critical two-dimensional Ising model with quenched random ferromagnetic couplings. Using replica calculations in the renormalization group framework we derive explicit expressions for the probability distribution function of the critical internal energy and for the specific heat fluctuations. It is shown that the disorder distribution of internal energies is Gaussian, and the typical sample-to-sample fluctuations as well as the average value scale with the system size L like ∼ L ln ln(L). In contrast, the specific heat is shown to be self-averaging with a distribution function that tends to a δ-peak in the thermodynamic limit L → ∞. While previously a lack of self-averaging was found for the free energy, we here obtain results for quantities that are directly measurable in simulations, and implications for measurements in the actual lattice system are discussed.</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-averaging in the random two-dimensional Ising ferromagnet","attachmentId":67128407,"attachmentType":"pdf","work_url":"https://www.academia.edu/48600954/Self_averaging_in_the_random_two_dimensional_Ising_ferromagnet","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/48600954/Self_averaging_in_the_random_two_dimensional_Ising_ferromagnet"><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="28790438" 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/28790438/3_DIMENSIONAL_Ferromagnetic_Ising_Models_with_Quenched_Random_Nonmagnetic_Impurities">3-DIMENSIONAL Ferromagnetic Ising-Models with Quenched, Random Nonmagnetic Impurities</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="50940" href="https://granada.academia.edu/JoaquinMarro">Joaquin Marro</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physica B & C, 1986</p><p class="ds-related-work--abstract ds2-5-body-sm">We investigate the thermal and magnetic properties of three-dimensional, ferromagnetic Ising models with quenched and random non-magnetic (site) impurities in the case of simple cubic lattices. The reported thermodynamic phase diagrams reveal in particular a sharp phase transition (e.g. in the magnetic susceptibility) for the (relatively small) impurity concentrations</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":"3-DIMENSIONAL Ferromagnetic Ising-Models with Quenched, Random Nonmagnetic Impurities","attachmentId":49208732,"attachmentType":"pdf","work_url":"https://www.academia.edu/28790438/3_DIMENSIONAL_Ferromagnetic_Ising_Models_with_Quenched_Random_Nonmagnetic_Impurities","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/28790438/3_DIMENSIONAL_Ferromagnetic_Ising_Models_with_Quenched_Random_Nonmagnetic_Impurities"><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="99439066" 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/99439066/The_low_temperature_behavior_of_disordered_magnets">The low-temperature behavior of disordered magnets</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="42709223" href="https://independent.academia.edu/JuergFroehlich">Juerg Froehlich</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Communications in Mathematical 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":"The low-temperature behavior of disordered magnets","attachmentId":100528596,"attachmentType":"pdf","work_url":"https://www.academia.edu/99439066/The_low_temperature_behavior_of_disordered_magnets","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/99439066/The_low_temperature_behavior_of_disordered_magnets"><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="76957714" 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/76957714/Self_averaging_in_the_random_2D_Ising_ferromagnet">Self-averaging in the random 2D Ising ferromagnet</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="3474085" href="https://nas.academia.edu/MaxymDudka">Maxym Dudka</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2017</p><p class="ds-related-work--abstract ds2-5-body-sm">We study sample-to-sample fluctuations in a critical two-dimensional Ising model with quenched random ferromagnetic couplings. Using replica calculations in the renormalization group framework we derive explicit expressions for the probability distribution function of the critical internal energy and for the specific heat fluctuations. It is shown that the disorder distribution of internal energies is Gaussian, and the typical sample-to-sample fluctuations as well as the average value scale with the system size L like ∼ L (L). In contrast, the specific heat is shown to be self-averaging with a distribution function that tends to a δ-peak in the thermodynamic limit L →∞. While previously a lack of self-averaging was found for the free energy, we here obtain results for quantities that are directly measurable in simulations, and implications for measurements in the actual lattice system are discussed.</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-averaging in the random 2D Ising ferromagnet","attachmentId":84472412,"attachmentType":"pdf","work_url":"https://www.academia.edu/76957714/Self_averaging_in_the_random_2D_Ising_ferromagnet","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/76957714/Self_averaging_in_the_random_2D_Ising_ferromagnet"><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="109145067" 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/109145067/Critical_disorder_and_critical_magnetic_field_of_the_nonequilibrium_athermal_random_field_Ising_model_in_thin_systems">Critical disorder and critical magnetic field of the nonequilibrium athermal random-field Ising model in thin systems</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="40901382" href="https://bg.academia.edu/DjordjeSpasojevic">Djordje Spasojevic</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical review, 2019</p><p class="ds-related-work--abstract ds2-5-body-sm">In the present study of the nonequilibrium athermal random-field Ising model we focus on the behavior of the critical disorder R c (l) and the critical magnetic field H c (l) under different boundary conditions when the system thickness l varies. We propose expressions for R c (l) and H c (l) as well as for the effective critical disorder R eff c (l, L) and effective critical magnetic field H eff c (l, L) playing the role of the effective critical parameters for the L × L × l lattices of finite lateral size L. We support these expressions by the scaling collapses of the magnetization and susceptibility curves obtained in extensive simulations. The collapses are achieved with the two-dimensional (2D) exponents for l below some characteristic value, providing thus a numerical evidence that the thin systems exhibit a 2D-like criticality which should be relevant for the experimental analyses of thin ferromagnetic samples.</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 disorder and critical magnetic field of the nonequilibrium athermal random-field Ising model in thin systems","attachmentId":107354894,"attachmentType":"pdf","work_url":"https://www.academia.edu/109145067/Critical_disorder_and_critical_magnetic_field_of_the_nonequilibrium_athermal_random_field_Ising_model_in_thin_systems","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/109145067/Critical_disorder_and_critical_magnetic_field_of_the_nonequilibrium_athermal_random_field_Ising_model_in_thin_systems"><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="30873647" 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/30873647/Universality_frustration_and_conformal_invariance_in_two_dimensional_random_Ising_magnets">Universality, frustration, and conformal invariance in two-dimensional random Ising magnets</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="58764247" href="https://ufrj.academia.edu/RaimundodosSantos">Raimundo dos Santos</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="58804473" href="https://independent.academia.edu/QueirozSde">S. de Queiroz</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="313597810" href="https://independent.academia.edu/FabioAar%C3%A3oReis">Fabio Aarão Reis</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review B, 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":"Universality, frustration, and conformal invariance in two-dimensional random Ising magnets","attachmentId":51300133,"attachmentType":"pdf","work_url":"https://www.academia.edu/30873647/Universality_frustration_and_conformal_invariance_in_two_dimensional_random_Ising_magnets","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/30873647/Universality_frustration_and_conformal_invariance_in_two_dimensional_random_Ising_magnets"><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":93554212,"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":93554212,"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_93554212" 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. 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