{
  "id": "1005.2088",
  "version": "v1",
  "published": "2010-05-12T13:25:35.000Z",
  "updated": "2010-05-12T13:25:35.000Z",
  "title": "Logarithmic two-point correlators in the Abelian sandpile model",
  "authors": [
    "V. S. Poghosyan",
    "S. Y. Grigorev",
    "V. B. Priezzhev",
    "P. Ruelle"
  ],
  "comment": "28 pages",
  "journal": "J.Stat.Mech.1007:P07025,2010",
  "doi": "10.1088/1742-5468/2010/07/P07025",
  "categories": [
    "cond-mat.stat-mech",
    "hep-th",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We present the detailed calculations of the asymptotics of two-site correlation functions for height variables in the two-dimensional Abelian sandpile model. By using combinatorial methods for the enumeration of spanning trees, we extend the well-known result for the correlation $\\sigma_{1,1} \\simeq 1/r^4$ of minimal heights $h_1=h_2=1$ to $\\sigma_{1,h} = P_{1,h}-P_1P_h$ for height values $h=2,3,4$. These results confirm the dominant logarithmic behaviour $\\sigma_{1,h} \\simeq (c_h\\log r + d_h)/r^4 + {\\cal O}(r^{-5})$ for large $r$, predicted by logarithmic conformal field theory based on field identifications obtained previously. We obtain, from our lattice calculations, the explicit values for the coefficients $c_h$ and $d_h$ (the latter are new).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-05-12T13:25:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.65.+b"
    ],
    "keywords": [
      "logarithmic two-point correlators",
      "logarithmic conformal field theory",
      "two-site correlation functions",
      "two-dimensional abelian sandpile model",
      "dominant logarithmic behaviour"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Statistical Mechanics: Theory and Experiment",
      "year": 2010,
      "month": "Jul",
      "volume": 2010,
      "number": 7,
      "pages": 7025
    },
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 855848,
      "adsabs": "2010JSMTE..07..025P"
    }
  }
}