The number of link and cluster states: the core of the 2D $q$ state Potts model

Details The number of link and cluster states: the core of the 2D $q$ state Potts model The number of link and cluster states: the core of the 2D $q$ state Potts model

2005-03-02

arxiv.org/abs/cond-mat/0503049v2

J. Phys. A, Math. Gen. 38 (2005) 10893-10904

Physics

Condensed Matter

Statistical Mechanics

Many updates throughout the text. Current version published in J. Phys. A

Scientific paper

10.1088/0305-4470/38/50/002

Due to Fortuin and Kastelyin the $q$ state Potts model has a representation as a sum over random graphs, generalizing the Potts model to arbitrary $q$ is based on this representation. A key element of the Random Cluster representation is the combinatorial factor $\Gamma_{\Graph{G}}(\Clusters,\Edges)$, which is the number of ways to form $\Clusters$ distinct clusters, consisting of totally $\Edges$ edges. We have devised a method to calculate $\Gamma_{\Graph{G}}(\Clusters,\Edges)$ from Monte Carlo simulations.

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