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Exact Potts Model Partition Functions for Strips of the Honeycomb Lattice
Authors:Shu-Chiuan Chang  Robert Shrock
Institution:(1) Department of Physics, National Cheng Kung University, Tainan, 70101, Taiwan;(2) Physics Division, National Center for Theoretical Science, National Taiwan University, Taipei, 10617, Taiwan;(3) C.N. Yang Institute for Theoretical Physics, State University of New York, Stony Brook, NY 11794-3840, USA
Abstract:We present exact calculations of the Potts model partition function Z(G,q,v) for arbitrary q and temperature-like variable v on strip graphs G of the honeycomb lattice for a variety of transverse widths equal to L y vertices and for arbitrarily great length, with free longitudinal boundary conditions and free and periodic transverse boundary conditions. These partition functions have the form $Z(G,q,v)=\sum_{j=1}^{N_{Z,G,\lambda}}c_{Z,G,j}(\lambda_{Z,G,j})^{m}$ , where m denotes the number of repeated subgraphs in the longitudinal direction. We give general formulas for N Z,G,j for arbitrary L y . 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. Plots of specific heat for infinite-length strips are also presented, and, in particular, the behavior of the Potts antiferromagnet at $q=(3+\sqrt{5}\ )/2$ is investigated.
Keywords:Potts model  Honeycomb lattice  Exact solutions  Transfer matrix
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