{
  "id": "cond-mat/9812243",
  "version": "v1",
  "published": "1998-12-15T09:10:35.000Z",
  "updated": "1998-12-15T09:10:35.000Z",
  "title": "Percolation-like phase transition in a non-equilibrium steady state",
  "authors": [
    "Indrani Bose",
    "Indranath Chaudhuri"
  ],
  "comment": "LaTeX, 12 pages, 7 PS figures, communicated to Phys. Rev E",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We study the Gierer-Meinhardt model of reaction-diffusion on a site-disordered square lattice. Let $p$ be the site occupation probability of the square lattice. For $p$ greater than a critical value $p_c$, the steady state consists of stripe-like patterns with long-range connectivity. For $p < p_c$, the connectivity is lost. The value of $p_c$ is found to be much greater than that of the site percolation threshold for the square lattice. In the vicinity of $p_c$, the cluster-related quantities exhibit power-law scaling behaviour. The method of finite-size scaling is used to determine the values of the fractal dimension $d_f$, the ratio, $\\frac{\\gamma}{\\nu}$, of the average cluster size exponent $\\gamma$ and the correlation length exponent $\\nu$ and also $\\nu$ itself. The values appear to indicate that the disordered GM model belongs to the universality class of ordinary percolation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-12-15T09:10:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-equilibrium steady state",
      "percolation-like phase transition",
      "square lattice",
      "site occupation probability",
      "disordered gm model belongs"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998cond.mat.12243B"
    }
  }
}