{
  "id": "1206.2312",
  "version": "v2",
  "published": "2012-06-11T18:55:08.000Z",
  "updated": "2012-07-22T09:17:13.000Z",
  "title": "Logarithmic observables in critical percolation",
  "authors": [
    "Romain Vasseur",
    "Jesper Lykke Jacobsen",
    "Hubert Saleur"
  ],
  "comment": "11 pages, 2 figures. V2: as published",
  "journal": "J. Stat. Mech. L07001 (2012)",
  "doi": "10.1088/1742-5468/2012/07/L07001",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Although it has long been known that the proper quantum field theory description of critical percolation involves a logarithmic conformal field theory (LCFT), no direct consequence of this has been observed so far. Representing critical bond percolation as the Q = 1 limit of the Q-state Potts model, and analyzing the underlying S_Q symmetry of the Potts spins, we identify a class of simple observables whose two-point functions scale logarithmically for Q = 1. The logarithm originates from the mixing of the energy operator with a logarithmic partner that we identify as the field that creates two propagating clusters. In d=2 dimensions this agrees with general LCFT results, and in particular the universal prefactor of the logarithm can be computed exactly. We confirm its numerical value by extensive Monte-Carlo simulations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-07-22T09:17:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.50.+q",
      "64.60.F-",
      "64.60.De",
      "11.25.Hf"
    ],
    "keywords": [
      "critical percolation",
      "logarithmic observables",
      "proper quantum field theory description",
      "logarithmic conformal field theory",
      "general lcft results"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Statistical Mechanics: Theory and Experiment",
      "year": 2012,
      "month": "Jul",
      "volume": 2012,
      "number": 7
    },
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1118090,
      "adsabs": "2012JSMTE..07..000V"
    }
  }
}