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The three-state Potts antiferromagnet on plane quadrangulations

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Modelización, Simulación Numérica y Matemática Industriales
dc.contributor.authorLv, Jian-Ping
dc.contributor.authorDeng, Youjin
dc.contributor.authorJacobsen, Jesper L.
dc.contributor.authorSalas Martínez, Jesús
dc.contributor.funderMinisterio de Economía y Competitividad (España)es
dc.date.accessioned2021-01-27T11:34:11Z
dc.date.available2021-01-27T11:34:11Z
dc.date.issued2018-07-21
dc.description.abstractWe study the antiferromagnetic 3-state Potts model on general (periodic) plane quadrangulations Gamma. Any quadrangulation can be built from a dual pair (G,G*). Based on the duality properties of G, we propose a new criterion to predict the phase diagram of this model. If Gamma is of self-dual type (i.e. if G is isomorphic to its dual G*), the model has a zero-temperature critical point with central charge c = 1, and it is disordered at all positive temperatures. If Gamma is of non-self-dual type (i.e. if G is not isomorphic to G*), three ordered phases coexist at low temperature, and the model is disordered at high temperature. In addition, there is a finite-temperature critical point (separating these two phases) which belongs to the universality class of the ferromagnetic 3-state Potts model with central charge c = 4 / 5. We have checked these conjectures by studying four (resp. seven) quadrangulations of self-dual (resp. non-self-dual) type, and using three complementary high-precision techniques: Monte-Carlo simulations, transfer matrices, and critical polynomials. In all cases, we find agreement with the conjecture. We have also found that the Wang-Swendsen-Kotecky Monte Carlo algorithm does not have (resp. does have) critical slowing down at the corresponding critical point on quadrangulations of self-dual (resp. non-self-dual) type.en
dc.description.sponsorshipThis work has been supported in part by the National Natural Science Foundation of China under grants No. 11774002 (JPL), and No. 11625522 (YD), the Key Projects of Anhui Province University Outstanding Youth Talent Support Program grant gxyqZD2017009 (JPL), the Ministry of Science and Technology of China grant No. 2016YFA0301600 (YD), the Institut Universitaire de France, and the European Research Council through the Advanced Grant NuQFT (JLJ), and the MINECO FIS2014-57387-C3-3-P and MINECO/AEI/FEDER, UE FIS2017-84440-C2-2-P grants (JLJ and JS).en
dc.format.extent44es
dc.identifier.bibliographicCitationJournal of Physics A, Mathematical and Theoretical, 51(36), 3650012, July 2018, 44 pp.en
dc.identifier.doihttps://doi.org/10.1088/1751-8121/aad1fe
dc.identifier.issn1751-8113
dc.identifier.issn1751-8121 (online)
dc.identifier.publicationfirstpage1es
dc.identifier.publicationissue36, 365001es
dc.identifier.publicationlastpage44es
dc.identifier.publicationtitleJournal of Physics A-Mathematical and Theoreticalen
dc.identifier.publicationvolume51es
dc.identifier.urihttps://hdl.handle.net/10016/31795
dc.identifier.uxxiAR/0000021688
dc.language.isoengen
dc.publisherIOP Publishing Ltd.en
dc.relation.hasversionhttps://arxiv.org/abs/1804.08911
dc.relation.projectIDGobierno de España. FIS2014-57387-C3-3-Pes
dc.relation.projectIDGobierno de España. FIS2017-84440-C2-2-Pes
dc.rights© 2018 IOP Publishing Ltd.es
dc.rights.accessRightsopen accessen
dc.subject.ecienciaMatemáticases
dc.subject.otherDualityen
dc.subject.otherPotts antiferromagneten
dc.subject.otherPlane quadrangulationen
dc.subject.otherTransfer matrixen
dc.subject.otherMonte Carlo simulationen
dc.subject.otherCritical polynomialen
dc.subject.otherWang-Swendsen-Koteky algorithmen
dc.titleThe three-state Potts antiferromagnet on plane quadrangulationsen
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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