General structural results for Potts model partition functions on lattice strips

Shu Chiuan Chang, Robert Shrock

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

We present a set of general results on structural features of the q-state Potts model partition function Z(G,q,v) for arbitrary q and temperature Boltzmann variable v for various lattice strips of arbitrarily great width Ly vertices and length Lx vertices, including (i) cyclic and Möbius strips of the square and triangular lattices, and (ii) self-dual cyclic strips of the square lattice. We also present an exact solution for the chromatic polynomial for the cyclic and Möbius strips of the square lattice with width Ly=5 (the greatest width for which an exact solution has been obtained so far for these families). In the Lx→∞ limit, we calculate the ground-state degeneracy per site, W(q) and determine the boundary ℬ across which W(q) is singular in the complex q plane.

Original languageEnglish
Pages (from-to)335-379
Number of pages45
JournalPhysica A: Statistical Mechanics and its Applications
Volume316
Issue number1-4
DOIs
Publication statusPublished - 2002 Dec 15

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Condensed Matter Physics

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