{
  "id": "0912.0719",
  "version": "v1",
  "published": "2009-12-03T19:45:19.000Z",
  "updated": "2009-12-03T19:45:19.000Z",
  "title": "The weak limit of Ising models on locally tree-like graphs",
  "authors": [
    "Andrea Montanari",
    "Elchanan Mossel",
    "Allan Sly"
  ],
  "comment": "16 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the Ising model with inverse temperature beta and without external field on sequences of graphs G_n which converge locally to the k-regular tree. We show that for such graphs the Ising measure locally weak converges to the symmetric mixture of the Ising model with + boundary conditions and the - boundary conditions on the k-regular tree with inverse temperature \\beta. In the case where the graphs G_n are expanders we derive a more detailed understanding by showing convergence of the Ising measure condition on positive magnetization (sum of spins) to the + measure on the tree.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-12-03T19:45:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ising model",
      "locally tree-like graphs",
      "weak limit",
      "boundary conditions",
      "k-regular tree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.0719M"
    }
  }
}