Transfer Matrices for the Zero-Temperature Potts Antiferromagnet on Cyclic and Mobius Lattice Strips

Details Transfer Matrices for the Zero-Temperature Potts Antiferromagnet on Cyclic and Mobius Lattice Strips Transfer Matrices for the Zero-Temperature Potts Antiferromagnet on Cyclic and Mobius Lattice Strips

2004-04-16

arxiv.org/abs/cond-mat/0404373v2

PHYSICA A 346, 400-450 (2005)

Physics

Condensed Matter

Statistical Mechanics

62 pages, latex, 6 eps figures, includes additional results, e.g., loci ${\cal B}$, requested by referee

Scientific paper

10.1016/j.physa.2004.08.010

We present transfer matrices for the zero-temperature partition function of the $q$-state Potts antiferromagnet (equivalently, the chromatic polynomial) on cyclic and M\"obius strips of the square, triangular, and honeycomb lattices of width $L_y$ and arbitrarily great length $L_x$. We relate these results to our earlier exact solutions for square-lattice strips with $L_y=3,4,5$, triangular-lattice strips with $L_y=2,3,4$, and honeycomb-lattice strips with $L_y=2,3$ and periodic or twisted periodic boundary conditions. We give a general expression for the chromatic polynomial of a M\"obius strip of a lattice $\Lambda$ and exact results for a subset of honeycomb-lattice transfer matrices, both of which are valid for arbitrary strip width $L_y$. New results are presented for the $L_y=5$ strip of the triangular lattice and the $L_y=4$ and $L_y=5$ strips of the honeycomb lattice. Using these results and taking the infinite-length limit $L_x \to \infty$, 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 $q$.

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