General structural results for Potts model partition functions on lattice strips

Shu-Chiuan Chang and Robert Shrock

Physica A: Statistical Mechanics and its Applications, 2002, vol. 316, issue 1, 335-379

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.

Keywords: Potts model; Tutte polynomial; Chromatic polynomial (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:316:y:2002:i:1:p:335-379

DOI: 10.1016/S0378-4371(02)01028-2

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