arXiv:cond-mat/0503049 Abstract

arXiv:cond-mat/0503049Abstract References Reviews Resources

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

Published 2005-03-02, updated 2005-12-01Version 2

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.

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

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

DOI: 10.1088/0305-4470/38/50/002

Categories: cond-mat.stat-mech

Keywords: state potts model, cluster states, monte carlo simulations, random cluster representation, random graphs

Tags: journal article

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