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Random Currents and Continuity of Ising Model’s Spontaneous Magnetization

Author(s): Aizenman, Michael; Duminil-Copin, Hugo; Sidoravicius, Vladas

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DC FieldValueLanguage
dc.contributor.authorAizenman, Michael-
dc.contributor.authorDuminil-Copin, Hugo-
dc.contributor.authorSidoravicius, Vladas-
dc.date.accessioned2019-05-30T15:59:42Z-
dc.date.available2019-05-30T15:59:42Z-
dc.date.issued2015-03en_US
dc.identifier.citationAizenman, Michael, Duminil-Copin, Hugo, Sidoravicius, Vladas. (2015). Random Currents and Continuity of Ising Model’s Spontaneous Magnetization. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 334 (719 - 742. doi:10.1007/s00220-014-2093-yen_US
dc.identifier.issn0010-3616-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr1s420-
dc.description.abstractThe spontaneous magnetization is proved to vanish continuously at the critical temperature for a class of ferromagnetic Ising spin systems which includes the nearest neighbor ferromagnetic Ising spin model on in d = 3 dimensions. The analysis also applies to higher dimensions, for which the result is already known, and to systems with interactions of power law decay. The proof employs in an essential way an extension of the Ising model’s random current representation to the model’s infinite volume limit. Using it, we relate the continuity of the magnetization to the vanishing of the free boundary condition Gibbs state’s long range order parameter. For reflection positive models the resulting criterion for continuity may be established through the infrared bound for all but the borderline lower dimensional cases. The exclusion applies to the one dimensional model with 1/r (2) interaction for which the spontaneous magnetization is known to be discontinuous at T (c) .en_US
dc.format.extent719 - 742en_US
dc.language.isoen_USen_US
dc.relation.ispartofCOMMUNICATIONS IN MATHEMATICAL PHYSICSen_US
dc.rightsAuthor's manuscripten_US
dc.titleRandom Currents and Continuity of Ising Model’s Spontaneous Magnetizationen_US
dc.typeJournal Articleen_US
dc.identifier.doidoi:10.1007/s00220-014-2093-y-
dc.date.eissued2014-07-03en_US
dc.identifier.eissn1432-0916-
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

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