{
  "id": "2003.02967",
  "version": "v1",
  "published": "2020-03-05T23:57:24.000Z",
  "updated": "2020-03-05T23:57:24.000Z",
  "title": "A Pfaffian formula for the Ising partition function of surface graphs",
  "authors": [
    "Anh Minh Pham"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We give a Pfaffian formula to compute the partition function of the Ising model on any graph $G$ embedded in a closed, possibly non-orientable surface. This formula, which is suitable for computational purposes, is based on the relation between the Ising model on $G$ and the dimer model on its terminal graph $G^T$. By combining the ideas of Loebl-Masbaum \\cite{Loeb11}, Tesler \\cite{Tes2000}, Cimasoni \\cite{Cim09, Cim10} and Chelkak-Cimasoni-Kassel \\cite{Chel15}, we give an elementary proof for the formula.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-05T23:57:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ising partition function",
      "pfaffian formula",
      "surface graphs",
      "ising model",
      "computational purposes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}