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Minimal bipartite dimers and higher genus Harnack curves

hal.structure.identifierLaboratoire de Probabilités, Statistique et Modélisation [LPSM (UMR_8001)]
dc.contributor.authorBoutillier, Cédric
hal.structure.identifierSection de mathématiques [Genève]
dc.contributor.authorCimasoni, David
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorde Tilière, Béatrice
dc.date.accessioned2022-02-18T14:31:54Z
dc.date.available2022-02-18T14:31:54Z
dc.date.issued2023
dc.identifier.issn2690-0998
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/22679
dc.language.isoenen
dc.subjectRiemann surfaces
dc.subjectM-curves
dc.subjectprime form
dc.subjectdimers
dc.subjectminimal graphs
dc.subject.ddc519en
dc.titleMinimal bipartite dimers and higher genus Harnack curves
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThis paper completes the comprehensive study of the dimer model on infinite minimal graphs with Fock's weights [arXiv:1503.00289] initiated in [arXiv:2007.14699]: the latter article dealt with the elliptic case, i.e. models whose associated spectral curve is of genus one, while the present work applies to models of arbitrary genus. This provides a far-reaching extension of the genus zero results of [arXiv:math-ph/0202018, arXiv:math/0311062], from isoradial graphs with critical weights to minimal graphs with weights defining an arbitrary spectral data. For any minimal graph with Fock's weights, we give an explicit local expression for a two-parameter family of inverses of the associated Kasteleyn operator. In the periodic case, this allows us to give local formulas for all ergodic Gibbs measures, thus providing an alternative description of the measures constructed in [arXiv:math-ph/0311005]. We also give formulas for the corresponding slopes, an explicit parametrisation of the spectral curve, and build on [arXiv:math/0311062, arXiv:1107.5588] to establish a correspondence between Fock's models on periodic minimal graphs and Harnack curves.
dc.publisher.cityParisen
dc.relation.isversionofjnlnameProbability and Mathematical Physics
dc.relation.isversionofjnldate2023
dc.relation.isversionofjnlpages58
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
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dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2023-02-04T09:49:34Z
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