Exact Potts model partition functions on ladder graphs

Robert Shrock

Physica A: Statistical Mechanics and its Applications, 2000, vol. 283, issue 3, 388-446

Abstract: We present exact calculations of the partition function Z of the q-state Potts model and its generalization to real q, for arbitrary temperature on n-vertex ladder graphs, i.e., strips of the square lattice with width Ly=2 and arbitrary length Lx, with free, cyclic, and Möbius longitudinal boundary conditions. These partition functions are equivalent to Tutte/Whitney polynomials for these graphs. The free energy is calculated exactly for the infinite-length limit of these ladder graphs and the thermodynamics is discussed. By comparison with strip graphs of other widths, we analyze how the singularities at the zero-temperature critical point of the ferromagnet on infinite-length, finite-width strips depend on the width. We point out and study the following noncommutativity at certain special values qs:limn→∞limq→qsZ1/n≠limq→qslimn→∞Z1/n. It is shown that the Potts antiferromagnet on both the infinite-length line and ladder graphs with cyclic or Möbius boundary conditions exhibits a phase transition at finite temperature if 0Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:283:y:2000:i:3:p:388-446

DOI: 10.1016/S0378-4371(00)00109-6

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