Exact Potts Model Partition Functions on Ladder Graphs

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.

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

References in corpus (2)

• T=0 Partition Functions for Potts Antiferromagnets on Square Lattice Strips with (Twisted) Periodic Boundary Conditions
• T=0 Partition Functions for Potts Antiferromagnets on Moebius Strips and Effects of Graph Topology

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