Phase diagram of the chromatic polynomial on a torus
نویسندگان
چکیده
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 squareand 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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