{
  "id": "0907.0777",
  "version": "v2",
  "published": "2009-07-04T16:53:07.000Z",
  "updated": "2009-07-13T00:39:20.000Z",
  "title": "Some Exact Results on the Potts Model Partition Function in a Magnetic Field",
  "authors": [
    "Shu-Chiuan Chang",
    "Robert Shrock"
  ],
  "comment": "5 pages, latex",
  "journal": "J. Phys. A 42, 385004 (2009)",
  "categories": [
    "cond-mat.stat-mech",
    "math.CO"
  ],
  "abstract": "We consider the Potts model in a magnetic field on an arbitrary graph $G$. Using a formula of F. Y. Wu for the partition function $Z$ of this model as a sum over spanning subgraphs of $G$, we prove some properties of $Z$ concerning factorization, monotonicity, and zeros. A generalization of the Tutte polynomial is presented that corresponds to this partition function. In this context we formulate and discuss two weighted graph-coloring problems. We also give a general structural result for $Z$ for cyclic strip graphs.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-07-13T00:39:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "potts model partition function",
      "magnetic field",
      "exact results",
      "cyclic strip graphs",
      "general structural result"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1751-8113/42/38/385004",
      "journal": "Journal of Physics A Mathematical General",
      "year": 2009,
      "month": "Sep",
      "volume": 42,
      "number": 38,
      "pages": 385004
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009JPhA...42L5004C"
    }
  }
}