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Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. II. Extended Results for Square-Lattice Chromatic Polynomial

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Abstract

We study the chromatic polynomials for m×n square-lattice strips, of width 9≤m≤13 (with periodic boundary conditions) and arbitrary length n (with free boundary conditions). We have used a transfer matrix approach that allowed us also to extract the limiting curves when n→∞. In this limit we have also obtained the isolated limiting points for these square-lattice strips and checked some conjectures related to 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

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  1. Jesper Lykke Jacobsen
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  2. Jesús Salas
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Jacobsen, J.L., Salas, J. Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. II. Extended Results for Square-Lattice Chromatic Polynomial. Journal of Statistical Physics 104, 701–723 (2001). https://doi.org/10.1023/A:1010328721905

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