General Structural Results for Potts Model Partition Functions on Lattice Strips

Details General Structural Results for Potts Model Partition Functions on Lattice Strips General Structural Results for Potts Model Partition Functions on Lattice Strips

2002-01-14

arxiv.org/abs/cond-mat/0201223v1

Physica A 316, 335-379 (2002)

Physics

Condensed Matter

Statistical Mechanics

49 pages, latex, four postscript figures

Scientific paper

10.1016/S0378-4371(02)01028-2

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 M\"obius 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 M\"obius 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 $L_x \to \infty$ 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.

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