{
  "id": "cond-mat/9702249",
  "version": "v2",
  "published": "1997-02-27T22:53:22.000Z",
  "updated": "1998-09-21T17:05:08.000Z",
  "title": "Comparison of rigidity and connectivity percolation in two dimensions",
  "authors": [
    "Cristian F. Moukarzel",
    "Phillip M. Duxbury"
  ],
  "comment": "RevTeX, 8 (A4) pages; epsfig figures. Entirely rewritten. Replaces \"Fractal backbone within...\" 1997 by the same authors",
  "journal": "Phys. Rev. E 59 (1999), 2614.",
  "doi": "10.1103/PhysRevE.59.2614",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.mtrl-sci"
  ],
  "abstract": "Using a recently developed algorithm for generic rigidity of two-dimensional graphs, we analyze rigidity and connectivity percolation transitions in two dimensions on lattices of linear size up to L=4096. We compare three different universality classes: The generic rigidity class; the connectivity class and; the generic ``braced square net''(GBSN). We analyze the spanning cluster density P_\\infty, the backbone density P_B and the density of dangling ends P_D. In the generic rigidity and connectivity cases, the load-carrying component of the spanning cluster, the backbone, is fractal at p_c, so that the backbone density behaves as B ~ (p-p_c)^{\\beta'} for p>p_c. We estimate \\beta'_{gr} = 0.25 +/- 0.02 for generic rigidity and \\beta'_c = 0.467 +/- 0.007 for the connectivity case. We find the correlation length exponents, \\nu_{gr} = 1.16 +/- 0.03 for generic rigidity compared to the exact value for connectivity \\nu_c = 4/3. In contrast the GBSN undergoes a first-order rigidity transition, with the backbone density being extensive at p_c, and undergoing a jump discontinuity on reducing p across the transition. We define a model which tunes continuously between the GBSN and GR classes and show that the GR class is typical.",
  "revisions": [
    {
      "version": "v2",
      "updated": "1998-09-21T17:05:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dimensions",
      "comparison",
      "connectivity case",
      "backbone density behaves",
      "connectivity percolation transitions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "RevTeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}