{
  "id": "1107.4982",
  "version": "v1",
  "published": "2011-07-25T15:41:30.000Z",
  "updated": "2011-07-25T15:41:30.000Z",
  "title": "Renormalization group treatment of rigidity percolation",
  "authors": [
    "R. B. Stinchcombe",
    "M. F Thorpe"
  ],
  "comment": "4 pages, 5 figures",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Renormalization group calculations are used to give exact solutions for rigidity percolation on hierarchical lattices. Algebraic scaling transformations for a simple example in two dimensions produce a transition of second order, with an unstable critical point and associated scaling laws. Values are provided for the order parameter exponent $\\beta = 0.0775$ associated with the spanning rigid cluster and also for $d \\nu = 3.533$ which is associated with an anomalous lattice dimension $d$ and the divergence in the correlation length near the transition. In addition we argue that the number of floppy modes $F$ plays the role of a free energy and hence find the exponent $\\alpha$ and establish hyperscaling. The exact analytical procedures demonstrated on the chosen example readily generalize to wider classes of hierarchical lattice.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-07-25T15:41:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "renormalization group treatment",
      "rigidity percolation",
      "renormalization group calculations",
      "hierarchical lattice",
      "order parameter exponent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.4982S"
    }
  }
}