{
  "id": "cond-mat/0503049",
  "version": "v2",
  "published": "2005-03-02T14:45:07.000Z",
  "updated": "2005-12-01T11:59:12.000Z",
  "title": "The number of link and cluster states: the core of the 2D $q$ state Potts model",
  "authors": [
    "J. Hove"
  ],
  "comment": "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"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-12-01T11:59:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "state potts model",
      "cluster states",
      "monte carlo simulations",
      "random cluster representation",
      "random graphs"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}