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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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| Authors: | Jesper Lykke Jacobsen Jesús Salas |
| Institution: | (1) Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris-Sud, Bâtiment 100, F-91405 Orsay, France;(2) Departamento de Física Teórica, Facultad de Ciencias, Universidad de Zaragoza, Zaragoza, 50009, Spain |
| Abstract: | We study the chromatic polynomials for m×n square-lattice strips, of width 9 m13 (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. |
| Keywords: | chromatic polynomial chromatic root antiferromagnetic Potts model square lattice transfer matrix Fortuin– Kasteleyn representation Beraha– Kahane– Weiss theorem Beraha numbers |
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