{
  "id": "cond-mat/0407276",
  "version": "v2",
  "published": "2004-07-11T13:57:42.000Z",
  "updated": "2004-10-01T10:45:40.000Z",
  "title": "Number of spanning clusters at the high-dimensional percolation thresholds",
  "authors": [
    "Santo Fortunato",
    "Amnon Aharony",
    "Antonio Coniglio",
    "Dietrich Stauffer"
  ],
  "comment": "8 pages, 11 figures. Final version to appear on Physical Review E",
  "doi": "10.1103/PhysRevE.70.056116",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn"
  ],
  "abstract": "A scaling theory is used to derive the dependence of the average number <k> of spanning clusters at threshold on the lattice size L. This number should become independent of L for dimensions d<6, and vary as log L at d=6. The predictions for d>6 depend on the boundary conditions, and the results there may vary between L^{d-6} and L^0. While simulations in six dimensions are consistent with this prediction (after including corrections of order loglog L), in five dimensions the average number of spanning clusters still increases as log L even up to L = 201. However, the histogram P(k) of the spanning cluster multiplicity does scale as a function of kX(L), with X(L)=1+const/L, indicating that for sufficiently large L the average <k> will approach a finite value: a fit of the 5D multiplicity data with a constant plus a simple linear correction to scaling reproduces the data very well. Numerical simulations for d>6 and for d=4 are also presented.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-10-01T10:45:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "high-dimensional percolation thresholds",
      "average number",
      "dimensions",
      "5d multiplicity data",
      "simple linear correction"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}