Exact potts model partition functions for strips of the honeycomb lattice

摘要

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) = Sigma(NZ,F,lambda)(j=1) C-Z,C-G,C-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+root 5)/2 is investigated.