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Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models

IV. Chromatic Polynomial with Cyclic Boundary Conditions

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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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Authors and Affiliations

  1. Laboratoire de Physique Théorique et Modéles Statistiques, Université Paris-Sud, Bâtiment 100, F-91405, Orsay, France

    Jesper Lykke Jacobsen

  2. Grupo de Modelización, Simulación Numérica y Matemática Industrial, Universidad Carlos III de Madrid, Avda. de la Universidad, 30, 28911, Leganés, Spain

    Jesús Salas

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  1. Jesper Lykke Jacobsen
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  2. Jesús Salas
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Correspondence to Jesper Lykke Jacobsen.

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Jacobsen, J.L., Salas, J. Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. J Stat Phys 122, 705–760 (2006). https://doi.org/10.1007/s10955-005-8077-8

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  • DOI: https://doi.org/10.1007/s10955-005-8077-8

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