Exact Potts Model Partition Functions on Ladder Graphs
Robert Shrock
Abstract
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 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.
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