{
  "id": "1712.04911",
  "version": "v1",
  "published": "2017-12-13T18:30:51.000Z",
  "updated": "2017-12-13T18:30:51.000Z",
  "title": "Statistical physics on a product of trees",
  "authors": [
    "Tom Hutchcroft"
  ],
  "comment": "11 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Let $G$ be the product of finitely many trees $T_1\\times T_2 \\cdots \\times T_N$, each of which is regular with degree at least three. We consider Bernoulli bond percolation and the Ising model on this graph, giving a short proof that the model undergoes a second order phase transition with mean-field critical exponents in each case. The result concerning percolation recovers a result of Kozma (2013), while the result concerning the Ising model is new. We also present a new proof, using similar techniques, of a lemma of Schramm concerning the decay of the critical two-point function along a random walk, as well as some generalizations of this lemma.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-13T18:30:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60B99"
    ],
    "keywords": [
      "statistical physics",
      "second order phase transition",
      "bernoulli bond percolation",
      "ising model",
      "model undergoes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}