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

Robert Shrock and Shan-Ho Tsai

Physica A: Statistical Mechanics and its Applications, 1998, vol. 259, issue 3, 315-348

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.

Keywords: Ground state entropy; Potts antiferromagnets (search for similar items in EconPapers)
Date: 1998
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:259:y:1998:i:3:p:315-348

DOI: 10.1016/S0378-4371(98)00359-8

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