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Exact Potts Model Partition Functions for Strips of the Honeycomb Lattice

By Shu-chiuan Chang and Robert Shrock

Abstract

We present exact calculations of the Potts model partition function Z(G,q,v) for arbitrary q and temperature-like variable v on n-vertex strip graphs G of the honeycomb lattice for a variety of transverse widths equal to Ly vertices and for arbitrarily great length, with free longitudinal boundary conditions and free and periodic transverse boundary conditions. These partition functions have the form Z(G,q,v) = ∑NZ,G,λ j=1 cZ,G,j(λZ,G,j) m, where m denotes the number of repeated subgraphs in the longitudinal direction. We give general formulas for NZ,G,j for arbitrary Ly. We also present plots of zeros of the partition function in the q plane for various values of v and in the v plane for various values of q. Explicit results for partition functions are given in the text for Ly = 2,3 (free) and Ly = 4 (cylindrical), and plots of partition function zeros are given for Ly up to 5 (free) and Ly = 6 (cylindrical). Plots of the internal energy and specifi

Year: 2008
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