Critical Binder cumulant and universality: Fortuin-Kasteleyn clusters and order-parameter fluctuations
We investigate the dependence of the critical Binder cumulant of the magnetization and the largest Fortuin-Kasteleyn cluster on the boundary conditions and aspect ratio of the underlying square Ising lattices. By means of the Swendsen-Wang algorithm, we generate numerical data for large system sizes...
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| description | We investigate the dependence of the critical Binder cumulant of the magnetization and the largest Fortuin-Kasteleyn cluster on the boundary conditions and aspect ratio of the underlying square Ising lattices. By means of the Swendsen-Wang algorithm, we generate numerical data for large system sizes and we perform a detailed finite-size scaling analysis for several values of the aspect ratio \(r\), for both periodic and free boundary conditions. We estimate the universal probability density functions of the largest Fortuin-Kasteleyn cluster and we compare it to those of the magnetization at criticality. It is shown that these probability density functions follow similar scaling laws, and it is found that the values of the critical Binder cumulant of the largest Fortuin-Kasteleyn cluster are upper bounds to the values of the respective order-parameter's cumulant, with a splitting behavior for large values of the aspect ratio. We also investigate the dependence of the amplitudes of the magnetization and the largest Fortuin-Kasteleyn cluster on the aspect ratio and boundary conditions. We find that the associated exponents, describing the aspect ratio dependencies, are different for the magnetization and the largest Fortuin-Kasteleyn cluster, but in each case are independent of boundary conditions. |
| doi_str_mv | 10.48550/arxiv.1310.4911 |
| format | Article |
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By means of the Swendsen-Wang algorithm, we generate numerical data for large system sizes and we perform a detailed finite-size scaling analysis for several values of the aspect ratio \(r\), for both periodic and free boundary conditions. We estimate the universal probability density functions of the largest Fortuin-Kasteleyn cluster and we compare it to those of the magnetization at criticality. It is shown that these probability density functions follow similar scaling laws, and it is found that the values of the critical Binder cumulant of the largest Fortuin-Kasteleyn cluster are upper bounds to the values of the respective order-parameter's cumulant, with a splitting behavior for large values of the aspect ratio. We also investigate the dependence of the amplitudes of the magnetization and the largest Fortuin-Kasteleyn cluster on the aspect ratio and boundary conditions. We find that the associated exponents, describing the aspect ratio dependencies, are different for the magnetization and the largest Fortuin-Kasteleyn cluster, but in each case are independent of boundary conditions.</description><identifier>EISSN: 2331-8422</identifier><identifier>DOI: 10.48550/arxiv.1310.4911</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Algorithms ; Aspect ratio ; Boundary conditions ; Clusters ; Dependence ; Free boundaries ; Ising model ; Lattices (mathematics) ; Magnetization ; Order parameters ; Physics - Statistical Mechanics ; Probability density functions ; Scaling laws ; Upper bounds ; Variation</subject><ispartof>arXiv.org, 2014-04</ispartof><rights>2014. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). 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We find that the associated exponents, describing the aspect ratio dependencies, are different for the magnetization and the largest Fortuin-Kasteleyn cluster, but in each case are independent of boundary conditions.</description><subject>Algorithms</subject><subject>Aspect ratio</subject><subject>Boundary conditions</subject><subject>Clusters</subject><subject>Dependence</subject><subject>Free boundaries</subject><subject>Ising model</subject><subject>Lattices (mathematics)</subject><subject>Magnetization</subject><subject>Order parameters</subject><subject>Physics - Statistical Mechanics</subject><subject>Probability density functions</subject><subject>Scaling laws</subject><subject>Upper bounds</subject><subject>Variation</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GOX</sourceid><recordid>eNotkE1Lw0AQhhdBsNTePcmC59T9bBJvWmwVC156D5PNLmzZbOJ-FPvvTVtPM7w8M7w8CD1QshSVlOQZwq89Lik_BzWlN2jGOKdFJRi7Q4sYD4QQtiqZlHyGzDrYZBU4_GZ9pwNWuc8OfMLgO5y9PeoQwdl0esGbIaRsffEFMWmnTx4rl6c1xAs8hOm-GCFAr6cQG5dVypDs4OM9ujXgol78zznab973649i9739XL_uCpC0LhQzojPCSKWZkVRI0OXUs6JVTRkvW85JCRVwbYDTuuXtqmXdigtDO6papfgcPV7fXhw0Y7A9hFNzdtGcXUzA0xUYw_CTdUzNYcjBT5UaRipBJKlpzf8AYkpj4g</recordid><startdate>20140403</startdate><enddate>20140403</enddate><creator>Malakis, A</creator><creator>Fytas, N G</creator><creator>Gülpinar, G</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>GOX</scope></search><sort><creationdate>20140403</creationdate><title>Critical Binder cumulant and universality: Fortuin-Kasteleyn clusters and order-parameter fluctuations</title><author>Malakis, A ; Fytas, N G ; Gülpinar, G</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a519-c2f4df4f5ce2f5145ae772581891237b3307a8a3efa319b3b6b2d634f1d1cbcc3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Algorithms</topic><topic>Aspect ratio</topic><topic>Boundary conditions</topic><topic>Clusters</topic><topic>Dependence</topic><topic>Free boundaries</topic><topic>Ising model</topic><topic>Lattices (mathematics)</topic><topic>Magnetization</topic><topic>Order parameters</topic><topic>Physics - Statistical Mechanics</topic><topic>Probability density functions</topic><topic>Scaling laws</topic><topic>Upper bounds</topic><topic>Variation</topic><toplevel>online_resources</toplevel><creatorcontrib>Malakis, A</creatorcontrib><creatorcontrib>Fytas, N G</creatorcontrib><creatorcontrib>Gülpinar, G</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>arXiv.org</collection><jtitle>arXiv.org</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Malakis, A</au><au>Fytas, N G</au><au>Gülpinar, G</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Critical Binder cumulant and universality: Fortuin-Kasteleyn clusters and order-parameter fluctuations</atitle><jtitle>arXiv.org</jtitle><date>2014-04-03</date><risdate>2014</risdate><eissn>2331-8422</eissn><abstract>We investigate the dependence of the critical Binder cumulant of the magnetization and the largest Fortuin-Kasteleyn cluster on the boundary conditions and aspect ratio of the underlying square Ising lattices. By means of the Swendsen-Wang algorithm, we generate numerical data for large system sizes and we perform a detailed finite-size scaling analysis for several values of the aspect ratio \(r\), for both periodic and free boundary conditions. We estimate the universal probability density functions of the largest Fortuin-Kasteleyn cluster and we compare it to those of the magnetization at criticality. It is shown that these probability density functions follow similar scaling laws, and it is found that the values of the critical Binder cumulant of the largest Fortuin-Kasteleyn cluster are upper bounds to the values of the respective order-parameter's cumulant, with a splitting behavior for large values of the aspect ratio. We also investigate the dependence of the amplitudes of the magnetization and the largest Fortuin-Kasteleyn cluster on the aspect ratio and boundary conditions. We find that the associated exponents, describing the aspect ratio dependencies, are different for the magnetization and the largest Fortuin-Kasteleyn cluster, but in each case are independent of boundary conditions.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><doi>10.48550/arxiv.1310.4911</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Algorithms Aspect ratio Boundary conditions Clusters Dependence Free boundaries Ising model Lattices (mathematics) Magnetization Order parameters Physics - Statistical Mechanics Probability density functions Scaling laws Upper bounds Variation |
| title | Critical Binder cumulant and universality: Fortuin-Kasteleyn clusters and order-parameter fluctuations |
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