Exact Potts Model Partition Functions on Ladder Graphs

Details Exact Potts Model Partition Functions on Ladder Graphs Exact Potts Model Partition Functions on Ladder Graphs

2000-01-26

arxiv.org/abs/cond-mat/0001389v1

Physica A283 (2000) 388-446

Physics

Condensed Matter

Statistical Mechanics

73 pages, Latex, 20 postscript figures, Physica A, in press

Scientific paper

10.1016/S0378-4371(00)00109-6

We present exact calculations of the partition function $Z$ of the $q$-state Potts model and its generalization to real $q$, the random cluster model, for arbitrary temperature on $n$-vertex ladder graphs with free, cyclic, and M\"obius 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.

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