{
  "id": "1208.4767",
  "version": "v1",
  "published": "2012-08-23T14:29:14.000Z",
  "updated": "2012-08-23T14:29:14.000Z",
  "title": "Some Exact Results on Bond Percolation",
  "authors": [
    "Shu-Chiuan Chang",
    "Robert Shrock"
  ],
  "comment": "33 pages latex 3 figures",
  "journal": "J. Stat. Phys. 149, 676-700 (2012)",
  "doi": "10.1007/s10955-012-0616-5",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn"
  ],
  "abstract": "We present some exact results on bond percolation. We derive a relation that specifies the consequences for bond percolation quantities of replacing each bond of a lattice $\\Lambda$ by $\\ell$ bonds connecting the same adjacent vertices, thereby yielding the lattice $\\Lambda_\\ell$. This relation is used to calculate the bond percolation threshold on $\\Lambda_\\ell$. We show that this bond inflation leaves the universality class of the percolation transition invariant on a lattice of dimensionality $d \\ge 2$ but changes it on a one-dimensional lattice and quasi-one-dimensional infinite-length strips. We also present analytic expressions for the average cluster number per vertex and correlation length for the bond percolation problem on the $N \\to \\infty$ limits of several families of $N$-vertex graphs. Finally, we explore the effect of bond vacancies on families of graphs with the property of bounded diameter as $N \\to \\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-08-23T14:29:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exact results",
      "bond percolation quantities",
      "percolation transition invariant",
      "bond percolation problem",
      "bond percolation threshold"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Statistical Physics",
      "year": 2012,
      "month": "Nov",
      "volume": 149,
      "number": 4,
      "pages": 676
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012JSP...149..676C"
    }
  }
}