T=0 Partition Functions for Potts Antiferromagnets on Square Lattice Strips with (Twisted) Periodic Boundary Conditions

Abstract

We present exact calculations of the zero-temperature partition function for the q-state Potts antiferromagnet (equivalently, the chromatic polynomial) for two families of arbitrarily long strip graphs of the square lattice with periodic boundary conditions in the transverse direction and (i) periodic (ii) twisted periodic boundary conditions in the longitudinal direction, so that the strip graphs are embedded on a (i) torus (ii) Klein bottle. In the limit of infinite length, we calculate the exponent of the entropy, W(q), show it to be the same for (i) and (ii), and determine its analytic structure.

7 pages, latex, one postscript figure

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• Yang-Lee Zeros of the Q-state Potts Model on Recursive Lattices
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• Transfer Matrices for the Partition Function of the Potts Model on Toroidal Lattice Strips
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• Transfer Matrices for the Zero-Temperature Potts Antiferromagnet on Cyclic and Mobius Lattice Strips
• Exact Chromatic Polynomials for Toroidal Chains of Complete Graphs
• Asymptotic Behavior of Acyclic and Cyclic Orientations of Directed Lattice Graphs
• Partition Function Zeros of a Restricted Potts Model on Lattice Strips and Effects of Boundary Conditions
• Lower Bounds on the Ground State Entropy of the Potts Antiferromagnet on Slabs of the Simple Cubic Lattice
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