{
  "id": "1109.0719",
  "version": "v1",
  "published": "2011-09-04T14:41:34.000Z",
  "updated": "2011-09-04T14:41:34.000Z",
  "title": "Combinatorial models of rigidity and renormalization",
  "authors": [
    "Julien Barré"
  ],
  "comment": "22 pages, 6 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We first introduce the percolation problems associated with the graph theoretical concepts of $(k,l)$-sparsity, and make contact with the physical concepts of ordinary and rigidity percolation. We then devise a renormalization transformation for $(k,l)$-percolation problems, and investigate its domain of validity. In particular, we show that it allows an exact solution of $(k,l)$-percolation problems on hierarchical graphs, for $k\\leq l<2k$. We introduce and solve by renormalization such a model, which has the interesting feature of showing both ordinary percolation and rigidity percolation phase transitions, depending on the values of the parameters.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-09-04T14:41:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "combinatorial models",
      "percolation problems",
      "rigidity percolation phase transitions",
      "ordinary percolation",
      "exact solution"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s10955-011-0394-5",
      "journal": "Journal of Statistical Physics",
      "year": 2012,
      "month": "Jan",
      "volume": 146,
      "number": 2,
      "pages": 359
    },
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012JSP...146..359B"
    }
  }
}