Exact Potts Model Partition Functions for Strips of the Honeycomb Lattice

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 , 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 is investigated.