{
  "id": "1011.1101",
  "version": "v2",
  "published": "2010-11-04T10:27:36.000Z",
  "updated": "2011-01-07T20:51:19.000Z",
  "title": "Factorization of correlations in two-dimensional percolation on the plane and torus",
  "authors": [
    "Robert M. Ziff",
    "Jacob J. H. Simmons",
    "Peter Kleban"
  ],
  "comment": "Small corrections (final version). In press, J. Phys. A",
  "journal": "J.Phys.A44:065002,2011",
  "doi": "10.1088/1751-8113/44/6/065002",
  "categories": [
    "cond-mat.dis-nn",
    "hep-lat",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Recently, Delfino and Viti have examined the factorization of the three-point density correlation function P_3 at the percolation point in terms of the two-point density correlation functions P_2. According to conformal invariance, this factorization is exact on the infinite plane, such that the ratio R(z_1, z_2, z_3) = P_3(z_1, z_2, z_3) [P_2(z_1, z_2) P_2(z_1, z_3) P_2(z_2, z_3)]^{1/2} is not only universal but also a constant, independent of the z_i, and in fact an operator product expansion (OPE) coefficient. Delfino and Viti analytically calculate its value (1.022013...) for percolation, in agreement with the numerical value 1.022 found previously in a study of R on the conformally equivalent cylinder. In this paper we confirm the factorization on the plane numerically using periodic lattices (tori) of very large size, which locally approximate a plane. We also investigate the general behavior of R on the torus, and find a minimum value of R approx. 1.0132 when the three points are maximally separated. In addition, we present a simplified expression for R on the plane as a function of the SLE parameter kappa.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-01-07T20:51:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "two-dimensional percolation",
      "factorization",
      "three-point density correlation function",
      "two-point density correlation functions",
      "operator product expansion"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2011,
      "month": "Feb",
      "volume": 44,
      "number": 6,
      "pages": "065002"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 875561,
      "adsabs": "2011JPhA...44f5002Z"
    }
  }
}