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Phase diagram of the chromatic polynomial on a torus

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URI: https://hdl.handle.net/10016/33064
ISSN: 0550-3213
DOI: https://doi.org/10.1016/j.nuclphysb.2007.04.023
UXXI: AR/0000005782
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Phase_NPB_2007_ps.pdf (1.27 MB)
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2007-11-05
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Elsevier
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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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Chromatic polynomial, Antiferromagnetic Potts model, Triangular lattice, Square lattice, Transfer matrix, Fortuin-Kasteleyn representation, Beraha numbers, Conformal field theory
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Jacobsen, J. L. & Salas, J. (2007). Phase diagram of the chromatic polynomial on a torus. Nuclear Physics B, 783(3), pp. 238–296.
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