{
  "id": "cond-mat/9904239",
  "version": "v1",
  "published": "1999-04-16T18:26:13.000Z",
  "updated": "1999-04-16T18:26:13.000Z",
  "title": "Universality class for bootstrap percolation with $m=3$ on the cubic lattice",
  "authors": [
    "N S Branco",
    "Cristiano J Silva"
  ],
  "comment": "11 pages; 4 figures; to appear in Int. J. Mod. Phys. C",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn"
  ],
  "abstract": "We study the $m=3$ bootstrap percolation model on a cubic lattice, using Monte Carlo simulation and finite-size scaling techniques. In bootstrap percolation, sites on a lattice are considered occupied (present) or vacant (absent) with probability $p$ or $1-p$, respectively. Occupied sites with less than $m$ occupied first-neighbours are then rendered unoccupied; this culling process is repeated until a stable configuration is reached. We evaluate the percolation critical probability, $p_c$, and both scaling powers, $y_p$ and $y_h$, and, contrarily to previous calculations, our results indicate that the model belongs to the same universality class as usual percolation (i.e., $m=0$). The critical spanning probability, $R(p_c)$, is also numerically studied, for systems with linear sizes ranging from L=32 up to L=480: the value we found, $R(p_c)=0.270 \\pm 0.005$, is the same as for usual percolation with free boundary conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-04-16T18:26:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cubic lattice",
      "universality class",
      "usual percolation",
      "monte carlo simulation",
      "bootstrap percolation model"
    ],
    "publication": {
      "doi": "10.1142/S0129183199000711",
      "journal": "International Journal of Modern Physics C",
      "year": 1999,
      "volume": 10,
      "number": 5,
      "pages": 921
    },
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999IJMPC..10..921B"
    }
  }
}