{
  "id": "1207.5500",
  "version": "v1",
  "published": "2012-07-23T19:56:29.000Z",
  "updated": "2012-07-23T19:56:29.000Z",
  "title": "The replica symmetric solution for Potts models on d-regular graphs",
  "authors": [
    "Amir Dembo",
    "Andrea Montanari",
    "Allan Sly",
    "Nike Sun"
  ],
  "comment": "23 pages",
  "categories": [
    "math.PR",
    "cond-mat.stat-mech"
  ],
  "abstract": "We provide an explicit formula for the limiting free energy density (log-partition function divided by the number of vertices) for ferromagnetic Potts models on uniformly sparse graph sequences converging locally to the d-regular tree for d even, covering all temperature regimes. This formula coincides with the Bethe free energy functional evaluated at a suitable fixed point of the belief propagation recursion on the d-regular tree, the so-called replica symmetric solution. For uniformly random d-regular graphs we further show that the replica symmetric Bethe formula is an upper bound for the asymptotic free energy for any model with permissive interactions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-07-23T19:56:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B20",
      "82B23",
      "05C80",
      "60K35"
    ],
    "keywords": [
      "replica symmetric solution",
      "potts models",
      "d-regular graphs",
      "free energy functional",
      "sparse graph sequences converging"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.5500D"
    }
  }
}