Phase diagram of the chromatic polynomial on a torus

Jesper Lykke Jacobsen; Jesus Salas

doi:10.1016/j.nuclphysb.2007.04.023

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arXiv · cond-mat/0703228

Phase diagram of the chromatic polynomial on a torus

Jesper Lykke Jacobsen·Jesus Salas

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Abstract

We study the zero-temperature partition function of the Potts antiferromagnet (i.e., the chromatic polynomial) on a torus using a transfer-matrix approach. We consider square- and triangular-lattice strips with fixed width L, arbitrary length N, and fully periodic boundary conditions. On the mathematical side, we obtain exact expressions for the chromatic polynomial of widths L=5,6,7 for the square and triangular lattices. On the physical side, we obtain the exact ``phase diagrams'' for these strips of width L and infinite length, and from these results we extract useful information about the infinite-volume phase diagram of this model: in particular, the number and position of the different phases.

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Jesper Lykke Jacobsen, Jesus Salas. 2007-05-21. Phase diagram of the chromatic polynomial on a torus. https://doi.org/10.1016/j.nuclphysb.2007.04.023

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