{
  "id": "math/0512523",
  "version": "v1",
  "published": "2005-12-22T12:41:38.000Z",
  "updated": "2005-12-22T12:41:38.000Z",
  "title": "Random-cluster representation of the Blume-Capel model",
  "authors": [
    "B. T. Graham",
    "G. R. Grimmett"
  ],
  "doi": "10.1007/s10955-006-9135-6",
  "categories": [
    "math.PR"
  ],
  "abstract": "The so-called diluted-random-cluster model may be viewed as a random-cluster representation of the Blume--Capel model. It has three parameters, a vertex parameter $a$, an edge parameter $p$, and a cluster weighting factor $q$. Stochastic comparisons of measures are developed for the `vertex marginal' when $q\\in[1,2]$, and the `edge marginal' when $q\\in[1,\\oo)$. Taken in conjunction with arguments used earlier for the random-cluster model, these permit a rigorous study of part of the phase diagram of the Blume--Capel model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-12-22T12:41:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B20"
    ],
    "keywords": [
      "blume-capel model",
      "random-cluster representation",
      "diluted-random-cluster model",
      "vertex parameter",
      "stochastic comparisons"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}