{
  "id": "cond-mat/0202144",
  "version": "v2",
  "published": "2002-02-08T15:19:15.000Z",
  "updated": "2002-08-01T16:27:52.000Z",
  "title": "Critical Percolation in High Dimensions",
  "authors": [
    "Peter Grassberger"
  ],
  "comment": "5 pages including figures, RevTeX",
  "doi": "10.1103/PhysRevE.67.036101",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn"
  ],
  "abstract": "We present Monte Carlo estimates for site and bond percolation thresholds in simple hypercubic lattices with 4 to 13 dimensions. For d<6 they are preliminary, for d >= 6 they are between 20 to 10^4 times more precise than the best previous estimates. This was achieved by three ingredients: (i) simple and fast hashing which allowed us to simulate clusters of millions of sites on computers with less than 500 MB memory; (ii) a histogram method which allowed us to obtain information for several p values from a single simulation; and (iii) a new variance reduction technique which is especially efficient at high dimensions where it reduces error bars by a factor up to approximately 30 and more. Based on these data we propose a new scaling law for finite cluster size corrections.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-08-01T16:27:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "high dimensions",
      "critical percolation",
      "monte carlo estimates",
      "finite cluster size corrections",
      "bond percolation thresholds"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "RevTeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}