Ground state entropy of Potts antiferromagnets on homeomorphic families of strip graphs

We present exact calculations of the zero-temperature partition function, and ground-state degeneracy (per site), W, for the q-state Potts antiferromagnet on a variety of homeomorphic families of planar strip graphs G = (Ch)(k1,k2,Sigma,k,m), where k(1), k(2), Sigma, and k describe the homeomorphic structure, and nz denotes the length of the ship. Several different ways of taking the total number of vertices to infinity, by sending (i) m --> infinity with k(1), k(2), and k fixed; (ii) k(1) and/or k(2) --> infinity with m, and k fixed; and (iii) k --> infinity with m and p = k(1) + k(2) fixed are studied and the respective loci of points B where W is nonanalytic in the complex q plane are determined. The B's for limit (i) are comprised of arcs which do not enclose regions in the q plane and, for many values of p and k, include support for Re(q)<0. The B for limits (ii) and (iii) is the unit circle \q - 1\ = 1. (C) 1998 Published by Elsevier Science B.V. All rights reserved.