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

Shu-Chiuan Chang, Robert Shrock
2005 Physica A: Statistical Mechanics and its Applications  
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 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
more » ... onditions. 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 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 →∞, 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.
doi:10.1016/j.physa.2004.08.010 fatcat:5chgzotvunftha3zco2kq33wrq