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Transfer matrices for the zero-temperature Potts antiferromagnet on cyclic and Möbius lattice strips

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  • Chang, Shu-Chiuan
  • Shrock, Robert

Abstract

We present transfer matrices for the zero-temperature partition function of the q-state Potts antiferromagnet (equivalently, the chromatic polynomial) on cyclic and Möbius strips of the square, triangular, and honeycomb lattices of width Ly and arbitrarily great length Lx. We relate these results to our earlier exact solutions for square-lattice strips with Ly=3,4,5, triangular-lattice strips with Ly=2,3,4, and honeycomb-lattice strips with Ly=2,3 and periodic or twisted periodic boundary conditions. We give a general expression for the chromatic polynomial of a Möbius strip of a lattice Λ and exact results for a subset of honeycomb-lattice transfer matrices, both of which are valid for arbitrary strip width Ly. New results are presented for the Ly=5 strip of the triangular lattice and the Ly=4 and Ly=5 strips of the honeycomb lattice. Using these results and taking the infinite-length limit Lx→∞, we determine the continuous accumulation locus of the zeros of the above partition function in the complex q plane, including the maximal real point of nonanalyticity of the degeneracy per site, W as a function of q.

Suggested Citation

  • Chang, Shu-Chiuan & Shrock, Robert, 2005. "Transfer matrices for the zero-temperature Potts antiferromagnet on cyclic and Möbius lattice strips," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 346(3), pages 400-450.
    • Handle: RePEc:eee:phsmap:v:346:y:2005:i:3:p:400-450
    DOI: 10.1016/j.physa.2004.08.010
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