Exact Potts model partition functions on wider arbitrary-length strips of the square lattice

Shu Chiuan Chang, Robert Shrock

Research output: Contribution to journalArticle

43 Citations (Scopus)

Abstract

We present exact calculations of the partition function of the q-state Potts model for general q and temperature on strips of the square lattice of width Ly=3 vertices and arbitrary length Lx with periodic longitudinal boundary conditions, of the following types: (i) (FBCy, PBCx)= cyclic, (ii) (FBCy, TPBCx)= Möbius, (iii) (PBCy, PBCx)= toroidal, and (iv) (PBCy, TPBCx)= Klein bottle, where FBC and (T)PBC refer to free and (twisted) periodic boundary conditions. Results for the Ly=2 torus and Klein bottle strips are also included. In the infinite-length limit the thermodynamic properties are discussed and some general results are given for low-temperature behavior on strips of arbitrarily great width. We determine the submanifold in the C2 space of q and temperature where the free energy is singular for these strips. Our calculations are also used to compute certain quantities of graph-theoretic interest.

Original languageEnglish
Pages (from-to)234-288
Number of pages55
JournalPhysica A: Statistical Mechanics and its Applications
Volume296
Issue number1-2
DOIs
Publication statusPublished - 2001 Jul 1

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Condensed Matter Physics

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