{
  "id": "cond-mat/0101112",
  "version": "v2",
  "published": "2001-01-09T11:31:12.000Z",
  "updated": "2001-03-30T15:07:53.000Z",
  "title": "Universal scaling functions for bond percolation on planar random and square lattices with multiple percolating clusters",
  "authors": [
    "Hsiao-Ping Hsu",
    "Simon C. Lin",
    "Chin-Kun Hu"
  ],
  "comment": "15 pages, 11 figures",
  "doi": "10.1103/PhysRevE.64.016127",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Percolation models with multiple percolating clusters have attracted much attention in recent years. Here we use Monte Carlo simulations to study bond percolation on $L_{1}\\times L_{2}$ planar random lattices, duals of random lattices, and square lattices with free and periodic boundary conditions, in vertical and horizontal directions, respectively, and with various aspect ratio $L_{1}/L_{2}$. We calculate the probability for the appearance of $n$ percolating clusters, $W_{n},$ the percolating probabilities, $P$, the average fraction of lattice bonds (sites) in the percolating clusters, $<c^{b}>_{n}$ ($<c^{s}>_{n}$), and the probability distribution function for the fraction $c$ of lattice bonds (sites), in percolating clusters of subgraphs with $n$ percolating clusters, $f_{n}(c^{b})$ ($f_{n}(c^{s})$). Using a small number of nonuniversal metric factors, we find that $W_{n}$, $P$, $<c^{b}>_{n}$ ($<c^{s}>_{n}$), and $f_{n}(c^{b})$ ($f_{n}(c^{s})$) for random lattices, duals of random lattices, and square lattices have the same universal finite-size scaling functions. We also find that nonuniversal metric factors are independent of boundary conditions and aspect ratios.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2001-03-30T15:07:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multiple percolating clusters",
      "square lattices",
      "universal scaling functions",
      "planar random",
      "bond percolation"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}