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Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. III. Triangular-Lattice Chromatic Polynomial

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Abstract

We study the chromatic polynomial P G (q) for m×n triangular-lattice strips of widths m≤12P,9F (with periodic or free transverse boundary conditions, respectively) and arbitrary lengths n (with free longitudinal boundary conditions). The chromatic polynomial gives the zero-temperature limit of the partition function for the q-state Potts antiferromagnet. We compute the transfer matrix for such strips in the Fortuin–Kasteleyn representation and obtain the corresponding accumulation sets of chromatic zeros in the complex q-plane in the limit n→∞. We recompute the limiting curve obtained by Baxter in the thermodynamic limit m,n→∞ and find new interesting features with possible physical consequences. Finally, we analyze the isolated limiting points and their relation with the Beraha numbers.

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Authors and Affiliations

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

    Jesper Lykke Jacobsen

  2. Departamento de Física Teórica, Facultad de Ciencias, Universidad de Zaragoza, Zaragoza, 50009, Spain

    Jesús Salas

  3. Department of Physics, New York University, 4 Washington Place, New York, New York, 10003

    Alan D. Sokal

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  1. Jesper Lykke Jacobsen
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  2. Jesús Salas
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  3. Alan D. Sokal
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Jacobsen, J.L., Salas, J. & Sokal, A.D. Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. III. Triangular-Lattice Chromatic Polynomial. Journal of Statistical Physics 112, 921–1017 (2003). https://doi.org/10.1023/A:1024611424456

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