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

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  • Shrock, Robert
  • Tsai, Shan-Ho

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.

Suggested Citation

  • Shrock, Robert & Tsai, Shan-Ho, 1999. "Ground-state degeneracy of Potts antiferromagnets: homeomorphic classes with noncompact W boundaries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 265(1), pages 186-223.
    • Handle: RePEc:eee:phsmap:v:265:y:1999:i:1:p:186-223
    DOI: 10.1016/S0378-4371(98)00568-8
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