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

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  • Shrock, Robert
  • Tsai, Shan-Ho

Abstract

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,Σ,k,m, where k1, 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 k1, k2, and k fixed; (ii) k1 and/or k2→∞ with m, and k fixed; and (iii) k→∞ with m and p=k1+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.

Suggested Citation

  • Shrock, Robert & Tsai, Shan-Ho, 1998. "Ground state entropy of Potts antiferromagnets on homeomorphic families of strip graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 259(3), pages 315-348.
    • Handle: RePEc:eee:phsmap:v:259:y:1998:i:3:p:315-348
    DOI: 10.1016/S0378-4371(98)00359-8
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    Cited by:

    1. Chang, Shu-Chiuan & Shrock, Robert, 2020. "Asymptotic behavior of acyclic and cyclic orientations of directed lattice graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).

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