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)_{k⊥,k2,Σ,k,m}, where k_⊥, k₂, Σ, and k describe the homeomorphic structure, and m denotes the length of the strip. Several different ways of taking the total number of vertices to infinity, by sending (i) m → ∞ with k_⊥, k₂, and k fixed; (ii) k⊥ and/or k₂ → ∞ with m, and k fixed; and (iii) k → ∞ with m and p = k_⊥ + k₂ 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.