{
  "id": "cond-mat/0203496",
  "version": "v1",
  "published": "2002-03-24T23:05:27.000Z",
  "updated": "2002-03-24T23:05:27.000Z",
  "title": "Convergence of threshold estimates for two-dimensional percolation",
  "authors": [
    "R. M. Ziff",
    "M. E. J. Newman"
  ],
  "comment": "11 pages, 4 figures",
  "journal": "Phys. Rev. E 66, 016129 (2002)",
  "doi": "10.1103/PhysRevE.66.016129",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Using a recently introduced algorithm for simulating percolation in microcanonical (fixed-occupancy) samples, we study the convergence with increasing system size of a number of estimates for the percolation threshold for an open system with a square boundary, specifically for site percolation on a square lattice. We show that the convergence of the so-called \"average-probability\" estimate is described by a non-trivial correction-to-scaling exponent as predicted previously, and measure the value of this exponent to be 0.90(2). For the \"median\" and \"cell-to-cell\" estimates of the percolation threshold we verify that convergence does not depend on this exponent, having instead a slightly faster convergence with a trivial analytic leading exponent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-03-24T23:05:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "two-dimensional percolation",
      "threshold estimates",
      "percolation threshold",
      "trivial analytic leading exponent",
      "square lattice"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}