Ground state entropy of the Potts antiferromagnet on strips of the square lattice

Shu Chiuan Chang, Robert Shrock

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)

Abstract

We present exact solutions for the zero-temperature partition function (chromatic polynomial P) and the ground state degeneracy per site W (= exponent of the ground-state entropy) for the q-state Potts antiferromagnet on strips of the square lattice of width Ly vertices and arbitrarily great length Lx vertices. The specific solutions are for (a) Ly = 4, (FBCy, PBCx) (cyclic); (b) Ly = 4, (FBCy, TPBCx) (Mobius); (c) Ly = 5,6, (PBCy, FBCx) (cylindrical); and (d) Ly = 5, (FBCy, FBCx) (open), where FBC, PBC, and TPBC denote free, periodic, and twisted periodic boundary conditions, respectively. In the Lx→∞ limit of each strip we discuss the analytic structure of W in the complex q plane. The respective W functions are evaluated numerically for various values of q. Several inferences are presented for the chromatic polynomials and analytic structure of W for lattice strips with arbitrarily great Ly. The absence of a nonpathological Lx→∞ limit for real nonintegral q in the interval 0<q<3 (0<q<4) for strips of the square (triangular) lattice is discussed.

Original languageEnglish
Pages (from-to)402-430
Number of pages29
JournalPhysica A: Statistical Mechanics and its Applications
Volume290
Issue number3-4
DOIs
Publication statusPublished - 2001 Feb 15

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Condensed Matter Physics

Fingerprint Dive into the research topics of 'Ground state entropy of the Potts antiferromagnet on strips of the square lattice'. Together they form a unique fingerprint.

Cite this