Publication: Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models VI. Square Lattice with Extra-Vertex Boundary Conditions
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2011-09
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Springer
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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.
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Chromatic polynomial, Chromatic roots, Tutte polynomial, Potts model, Transfer matrix, Beraha-Kahane-Weiss theorem, Planar graph, Square lattice, Extra-Vertex boundary conditions
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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.