General structural results for Potts model partition functions on lattice strips

2002/01/14 by Shu-Chiuan Chang, Robert Shrock · 1 citation
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Mathematical functions and polynomials #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1016/s0378-4371(02)01028-2

published as Physica A 316, 335-379 (2002) · 49 pages, latex, four postscript figures

arxiv created 2002/01/14 · openalex publication_date 2002/12/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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 L_y vertices and length L_x vertices, including (i) cyclic and Möbius strips of the square and triangular lattice, 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 L_y=5 (the greatest width for which an exact solution has been obtained so far for these families). In the L_x → ∞ limit, we calculate the ground-state degeneracy per site, W(q) and determine the boundary \cal B across which W(q) is singular in the complex q plane.

Citations

• Complex-temperature phase diagrams for theq-state Potts model on self-dual families of graphs and the nature of theq→∞limit
• Ground State Entropy of the Potts Antiferromagnet on Triangular Lattice Strips
• Some generalized order-disorder transformations
• A Contribution to the Theory of Chromatic Polynomials
• A Determinant Formula for the Number of Ways of Coloring a Map

Cited by

• Lower bounds on the ground-state entropy of the Potts antiferromagnet on slabs of the simple cubic lattice