{
  "id": "math-ph/0510025",
  "version": "v2",
  "published": "2005-10-06T14:19:53.000Z",
  "updated": "2006-02-25T20:00:38.000Z",
  "title": "On Gibbs Measures of $P$-Adic Potts Model on the Cayley Tree",
  "authors": [
    "Farrukh Mukhamedov",
    "Utkir Rozikov"
  ],
  "comment": "15 pages",
  "journal": "Indag.Math.15:85-100,2004",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider a nearest-neighbor $p$-adic Potts (with $q\\geq 2$ spin values and coupling constant $J\\in \\Q_p$) model on the Cayley tree of order $k\\geq 1$. It is proved that a phase transition occurs at $k=2$, $q\\in p\\mathbb{N}$ and $p\\geq 3$ (resp. $q\\in 2^2\\mathbb{N}$, $p=2$). It is established that for $p$-adic Potts model at $k\\geq 3$ a phase transition may occur only at $q\\in p\\mathbb{N}$ if $p\\geq 3$ and $q\\in 2^2\\mathbb{N}$ if $p=2$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-02-25T20:00:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46S10",
      "82B26",
      "12J12"
    ],
    "keywords": [
      "adic potts model",
      "cayley tree",
      "gibbs measures",
      "phase transition occurs",
      "spin values"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/S0019-3577(04)90007-9"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 867004,
      "adsabs": "2005math.ph..10025M"
    }
  }
}