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Transfer matrices and partition-function zeros for antiferromagnetic Potts models. V. Further results for the square-lattice chromatic polynomial

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Modelización, Simulación Numérica y Matemática Industriales
dc.contributor.authorSalas Martínez, Jesús
dc.contributor.authorSokal, Alan D.
dc.date.accessioned2021-07-14T10:20:51Z
dc.date.available2021-07-14T10:20:51Z
dc.date.issued2009-04
dc.description.abstractWe derive some new structural results for the transfer matrix of square-lattice Potts models with free and cylindrical boundary conditions. In particular, we obtain explicit closed-form expressions for the dominant (at large |q|) diagonal entry in the transfer matrix, for arbitrary widths m, as the solution of a special one-dimensional polymer model. We also obtain the large-q expansion of the bulk and surface (resp. corner) free energies for the zero-temperature antiferromagnet (= chromatic polynomial) through order q −47 (resp. q −46). Finally, we compute chromatic roots for strips of widths 9≤m≤12 with free boundary conditions and locate roughly the limiting curves.en
dc.format.extent95
dc.identifier.bibliographicCitationSalas, J. & Sokal, A. D. (2009). Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models V. Further Results for the Square-Lattice Chromatic Polynomial. Journal of Statistical Physics, 135(2), pp. 279–373.en
dc.identifier.doihttps://doi.org/10.1007/s10955-009-9725-1
dc.identifier.issn0022-4715
dc.identifier.publicationfirstpage279
dc.identifier.publicationissue2
dc.identifier.publicationlastpage373
dc.identifier.publicationtitleJournal of Statistical Physicsen
dc.identifier.publicationvolume135
dc.identifier.urihttps://hdl.handle.net/10016/33063
dc.identifier.uxxiAR/0000006537
dc.language.isoeng
dc.publisherSpringeren
dc.rights© 2009, Springer Science Business Media, LLCen
dc.rights.accessRightsopen accessen
dc.subject.ecienciaIngeniería Industriales
dc.subject.ecienciaMatemáticases
dc.subject.otherChromatic polynomialen
dc.subject.otherChromatic rooten
dc.subject.otherAntiferromagnetic Potts modelen
dc.subject.otherSquare latticeen
dc.subject.otherTransfer matrixen
dc.subject.otherFortuin-Kasteleyn representationen
dc.subject.otherBeraha-Kahane-Weiss theoremen
dc.subject.otherLarge-q expansionen
dc.subject.otherOne-dimensional polymer modelen
dc.subject.otherFinite lattice methoden
dc.titleTransfer matrices and partition-function zeros for antiferromagnetic Potts models. V. Further results for the square-lattice chromatic polynomialen
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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