The number of link and cluster states: the core of the 2D state Potts model
arXiv:cond-mat/0503049 · doi:10.1088/0305-4470/38/50/002
Abstract
Due to Fortuin and Kastelyin the state Potts model has a representation as a sum over random graphs, generalizing the Potts model to arbitrary is based on this representation. A key element of the Random Cluster representation is the combinatorial factor $Γ_{\Graph{G}}(\Clusters,\Edges)$, which is the number of ways to form $\Clusters$ distinct clusters, consisting of totally $\Edges$ edges. We have devised a method to calculate $Γ_{\Graph{G}}(\Clusters,\Edges)$ from Monte Carlo simulations.
Many updates throughout the text. Current version published in J. Phys. A