{
  "id": "1208.5325",
  "version": "v4",
  "published": "2012-08-27T08:26:19.000Z",
  "updated": "2013-07-19T08:08:12.000Z",
  "title": "The signed loop approach to the Ising model: foundations and critical point",
  "authors": [
    "Wouter Kager",
    "Marcin Lis",
    "Ronald Meester"
  ],
  "comment": "38 pages, 7 figures, with an improved Introduction. The final publication is available at link.springer.com",
  "journal": "J. Stat. Phys. 152 (2) pp. 353-387 (2013)",
  "doi": "10.1007/s10955-013-0767-z",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The signed loop method is a beautiful way to rigorously study the two-dimensional Ising model with no external field. In this paper, we explore the foundations of the method, including details that have so far been neglected or overlooked in the literature. We demonstrate how the method can be applied to the Ising model on the square lattice to derive explicit formal expressions for the free energy density and two-point functions in terms of sums over loops, valid all the way up to the self-dual point. As a corollary, it follows that the self-dual point is critical both for the behaviour of the free energy density, and for the decay of the two-point functions.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-07-19T08:08:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B20",
      "60C05"
    ],
    "keywords": [
      "ising model",
      "signed loop approach",
      "critical point",
      "free energy density",
      "foundations"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Statistical Physics",
      "year": 2013,
      "month": "Jul",
      "volume": 152,
      "number": 2,
      "pages": 353
    },
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013JSP...152..353K"
    }
  }
}