Phase diagram of the chromatic polynomial on a torus

Details Phase diagram of the chromatic polynomial on a torus Phase diagram of the chromatic polynomial on a torus

2007-03-09

arxiv.org/abs/cond-mat/0703228v2

Nucl.Phys.B783:238-296,2007

Physics

Condensed Matter

Statistical Mechanics

72 pages (LaTeX2e). Includes tex file, three sty files, and 26 Postscript figures. Also included are Mathematica files transfe

Scientific paper

10.1016/j.nuclphysb.2007.04.023

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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