{
  "id": "cond-mat/9709082",
  "version": "v1",
  "published": "1997-09-05T20:47:00.000Z",
  "updated": "1997-09-05T20:47:00.000Z",
  "title": "Violation of Scaling in the Contact Process with Quenched Disorder",
  "authors": [
    "Ronald Dickman",
    "Adriana G. Moreira"
  ],
  "comment": "13 pages, revtex, 7 postscript figures",
  "doi": "10.1103/PhysRevE.57.1263",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We study the two-dimensional contact process (CP) with quenched disorder (DCP), and determine the static critical exponents beta and nu_perp. The dynamic behavior is incompatible with scaling, as applied to models (such as the pure CP) that have a continuous phase transition to an absorbing state. We find that the survival probability (starting with all sites occupied), for a finite-size system at critical, decays according to a power law, as does the off-critical density autocorrelation function. Thus the critical exponent nu_parallle, which governs the relaxation time, is undefined, since the characteristic relaxation time is itself undefined. The logarithmic time-dependence found in recent simulations of the critical DCP [Moreira and Dickman, Phys. Rev. E54, R3090 (1996)] is further evidence of violation of scaling. A simple argument based on percolation cluster statistics yields a similar logarithmic evolution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1997-09-05T20:47:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quenched disorder",
      "percolation cluster statistics yields",
      "two-dimensional contact process",
      "similar logarithmic evolution",
      "characteristic relaxation time"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "RevTeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}