{
  "id": "1211.1521",
  "version": "v3",
  "published": "2012-11-07T12:22:21.000Z",
  "updated": "2013-01-11T01:53:30.000Z",
  "title": "Duality with real-space renormalization and its application to bond percolation",
  "authors": [
    "Masayuki Ohzeki"
  ],
  "comment": "10 pages, 9 figures",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech"
  ],
  "abstract": "We obtain the exact solution of the bond-percolation thresholds with inhomogenous probabilities on the square lattice. Our method is based on the duality analysis with real-space renormalization, which is a profound technique invented in the spin-glass theory. Our formulation is a more straightforward way compared to the very recent study on the same problem [R. M. Ziff, et. al., J. Phys. A: Math. Theor. 45 (2012) 494005]. The resultant generic formulas from our derivation can give several estimations for the bond-percolation thresholds on other lattices rather than the square lattice.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-01-11T01:53:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "64.60.ah"
    ],
    "keywords": [
      "real-space renormalization",
      "bond percolation",
      "application",
      "bond-percolation thresholds",
      "square lattice"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1103/PhysRevE.87.012137",
      "journal": "Physical Review E",
      "year": 2013,
      "month": "Jan",
      "volume": 87,
      "number": 1,
      "pages": "012137"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013PhRvE..87a2137O"
    }
  }
}