Publication: Transfer matrices and partition-function zeros for antiferromagnetic Potts models. IV. Chromatic polynomial with cyclic boundary conditions
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2006-02
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Springer
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Abstract
We study the chromatic polynomial P G (q) for m× n square- and triangular-lattice strips of widths 2≤ m ≤ 8 with cyclic boundary conditions. This polynomial gives the zero-temperature limit of the partition function for the antiferromagnetic q-state Potts model defined on the lattice G. We show how to construct the transfer matrix in the Fortuin–Kasteleyn representation for such lattices and obtain the accumulation sets of chromatic zeros in the complex q-plane in the limit n→∞. We find that the different phases that appear in this model can be characterized by a topological parameter. We also compute the bulk and surface free energies and the central charge.
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Chromatic polynomial, Antiferromagnetic Potts model, Triangular lattice, Square lattice, Transfer matrix, Fortuin-Kasteleyn representation, Beraha numbers, Conformal field theory
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Jacobsen, J. L. & Salas, J. (2006). Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models IV. Chromatic Polynomial with Cyclic Boundary Conditions. Journal of Statistical Physics, 122(4), pp. 705–760.