Ground-state degeneracy of Potts antiferromagnets: homeomorphic classes with noncompact W boundaries

Robert Shrock and Shan-Ho Tsai

Physica A: Statistical Mechanics and its Applications, 1999, vol. 265, issue 1, 186-223

Abstract: We present exact calculations of the zero-temperature partition function Z(G,q,T=0) and ground-state degeneracy W({G},q) for the q-state Potts antiferromagnet on a number of families of graphs G for which (generalizing q from Z+ to C) the boundary B of regions of analyticity of W in the complex q plane is noncompact, passing through z=1/q=0. For these types of graphs, since the reduced function Wred=q−1W is nonanalytic at z=0, there is no large-q Taylor series expansion of Wred. The study of these graphs thus gives insight into the conditions for the validity of the large-q expansions. It is shown how such (families of) graphs can be generated from known families by homeomorphic expansion.

Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:265:y:1999:i:1:p:186-223

DOI: 10.1016/S0378-4371(98)00568-8

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