Ground State Entropy of Potts Antiferromagnets: Cases with Noncompact W Boundaries Having Multiple Points at 1/q = 0

Abstract

We present exact calculations of the zero-temperature partition function, $Z(G,q,T=0)$, and ground-state degeneracy (per site), $W(G,q)$, for the $q$-state Potts antiferromagnet on a number of families of graphs $G$ for which the boundary $\mathcal{B}$ of regions of analyticity of $W$ in the complex $q$ plane is noncompact and has the properties that (i) in the $z=1/q$ plane, the point $z=0$ is a multiple point on $\mathcal{B}$ and (ii) $\mathcal{B}$ includes support for $Re(q)<0$. These families are generated by the method of homeomorphic expansion. Our results give further insight into the conditions for the validity of large--$q$ series expansions for the reduced function $W_{red.}=q^{-1}W$.

Comments: 29 pages, Latex, 10 encapsulated postscript figures, J. Phys. A, in press