Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models VI. Square Lattice with Extra-Vertex Boundary Conditions

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dc.contributor.author Salas Martínez, Jesús
dc.contributor.author Sokal, Alan D.
dc.date.accessioned 2021-07-13T13:04:22Z
dc.date.available 2021-07-13T13:04:22Z
dc.date.issued 2011-09
dc.identifier.bibliographicCitation Salas, J. & Sokal, A. D. (2011). Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models VI. Square Lattice with Extra-Vertex Boundary Conditions. Journal of Statistical Physics, 144(5), pp. 1028–1122.
dc.identifier.issn 0022-4715
dc.identifier.uri http://hdl.handle.net/10016/33053
dc.description.abstract We study, using transfer-matrix methods, the partition-function zeros of the square-lattice q-state Potts antiferromagnet at zero temperature (= square-lattice chromatic polynomial) for the boundary conditions that are obtained from an m×n grid with free boundary conditions by adjoining one new vertex adjacent to all the sites in the leftmost column and a second new vertex adjacent to all the sites in the rightmost column. We provide numerical evidence that the partition-function zeros are becoming dense everywhere in the complex q-plane outside the limiting curve B∞(sq) for this model with ordinary (e.g. free or cylindrical) boundary conditions. Despite this, the infinite-volume free energy is perfectly analytic in this region.
dc.format.extent 95
dc.language.iso eng
dc.publisher Springer
dc.rights © 2011, Springer Science Business Media, LLC.
dc.subject.other Chromatic polynomial
dc.subject.other Chromatic roots
dc.subject.other Tutte polynomial
dc.subject.other Potts model
dc.subject.other Transfer matrix
dc.subject.other Beraha-Kahane-Weiss theorem
dc.subject.other Planar graph
dc.subject.other Square lattice
dc.subject.other Extra-Vertex boundary conditions
dc.title Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models VI. Square Lattice with Extra-Vertex Boundary Conditions
dc.type article
dc.subject.eciencia Matemáticas
dc.identifier.doi https://doi.org/10.1007/s10955-011-0292-x
dc.rights.accessRights openAccess
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 1028
dc.identifier.publicationissue 5
dc.identifier.publicationlastpage 1122
dc.identifier.publicationtitle Journal of Statistical Physics
dc.identifier.publicationvolume 144
dc.identifier.uxxi AR/0000009531
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