{
  "id": "1504.01265",
  "version": "v1",
  "published": "2015-04-06T11:30:45.000Z",
  "updated": "2015-04-06T11:30:45.000Z",
  "title": "Boundary conditions for translation-invariant Gibbs measures of the Potts model on Cayley trees",
  "authors": [
    "D. Gandolfo",
    "M. M. Rakhmatullaev",
    "U. A. Rozikov"
  ],
  "comment": "13 pages, 6 figures",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider translation-invariant splitting Gibbs measures (TISGMs) for the $q$-state Potts model on a Cayley tree. Recently a full description of the TISGMs was obtained, and it was shown in particular that at sufficiently low temperatures their number is $2^{q}-1$. In this paper for each TISGM $\\mu$ we explicitly give the set of boundary conditions such that limiting Gibbs measures with respect to these boundary conditions coincide with $\\mu$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-06T11:30:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "translation-invariant gibbs measures",
      "cayley tree",
      "translation-invariant splitting gibbs measures",
      "state potts model",
      "boundary conditions coincide"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150401265G"
    }
  }
}