{
  "id": "1210.7311",
  "version": "v1",
  "published": "2012-10-27T10:44:30.000Z",
  "updated": "2012-10-27T10:44:30.000Z",
  "title": "Phase Transitions for a model with uncountable set of spin values on a Cayley tree",
  "authors": [
    "Yu. Kh. Eshkabilov",
    "U. A. Rozikov",
    "G. I. Botirov"
  ],
  "comment": "10 pages. arXiv admin note: substantial text overlap with arXiv:1202.2542, arXiv:1202.1722",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper we consider a model with nearest-neighbor interactions and with the set $[0,1]$ of spin values, on a Cayley tree of order $k \\geq 2$. To study translation-invariant Gibbs measures of the model we drive an nonlinear functional equation. For $k=2$ and 3 under some conditions on parameters of the model we prove non-uniqueness of translation-invariant Gibbs measures (i.e. there are phase transitions).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-27T10:44:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B05",
      "82B20",
      "60K35"
    ],
    "keywords": [
      "phase transitions",
      "spin values",
      "cayley tree",
      "uncountable set",
      "study translation-invariant gibbs measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.7311E"
    }
  }
}