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percolation theory bringing it into the framework of a general, renormalization-group-based, scaling scheme for systems above their upper critical dimensions d c. Behaviour at the critical point is non-universal in d \u003e d c = 6 dimensions. Proliferation of the largest clusters, with fractal dimension 4, is associated with the breakdown of hyperscaling there when free boundary conditions are used. But when the boundary conditions are periodic, the maximal clusters have dimension D = 2d/3, and obey random-graph asymptotics. Universality is instead manifest at the pseudocritical point, where the failure of hyperscaling in its traditional form is universally associated with random-graph-type asymptotics for critical cluster sizes, independent of boundary conditions.","publication_date":"2017,,","publication_name":"Journal of Physics A: Mathematical and Theoretical","grobid_abstract_attachment_id":"85220366"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Universal finite-size scaling for percolation theory in high dimensions","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [57856370]; 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.loswp.appleClientId = 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Using the scaling hypothesis that the ratio / of the mean cluster sizes M1 and M2 scales as f ((p - pc) L1/ν), we employ finite-size scaling analysis to find that / is nonuniversal with respect to the boundary conditions imposed. The mean of the ratios behaves similarly although with a distinct critical value reflecting the relevance of mass fluctuations at the percolation threshold. 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possible types of scaling limits for the collection of all percolation interfaces in the plane: (1) a trivial one, consisting of no curves at all, (2) a critical one, in which all points of the plane are surrounded by arbitrarily large loops and every deterministic point is almost surely surrounded</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":"Trivial, Critical and Near-critical Scaling Limits of Two-dimensional Percolation","attachmentId":79372633,"attachmentType":"pdf","work_url":"https://www.academia.edu/69177707/Trivial_Critical_and_Near_critical_Scaling_Limits_of_Two_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-wsj-grid-card-view-pdf" href="https://www.academia.edu/69177707/Trivial_Critical_and_Near_critical_Scaling_Limits_of_Two_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-wsj-grid-card" data-collection-position="7" data-entity-id="69177699" 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/69177699/The_full_scaling_limit_of_two_dimensional_critical_percolation">The full scaling limit of two-dimensional critical 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">Arxiv preprint math/0504036, 2005</p><p class="ds-related-work--abstract ds2-5-body-sm">Abstract: We use SLE (6) paths to construct a process of continuum nonsimple loops in the plane and prove that this process coincides with the full continuum scaling limit of 2D critical site percolation on the triangular lattice--that is, the scaling limit of the set of all interfaces ...</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 full scaling limit of two-dimensional critical percolation","attachmentId":79372644,"attachmentType":"pdf","work_url":"https://www.academia.edu/69177699/The_full_scaling_limit_of_two_dimensional_critical_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/69177699/The_full_scaling_limit_of_two_dimensional_critical_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="8" data-entity-id="69177700" 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/69177700/The_scaling_limit_geometry_of_near_critical_2D_percolation">The scaling limit geometry of near-critical 2D 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">Journal of statistical physics, 2006</p><p class="ds-related-work--abstract ds2-5-body-sm">We analyze the geometry of scaling limits of near-critical 2D percolation, ie, for p= p c+ λδ 1/ν, with ν= 4/3, as the lattice spacing δ→ 0. Our proposed framework extends previous analyses for p= pc, based on SLE 6. 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