{
  "id": "1207.4355",
  "version": "v1",
  "published": "2012-07-18T12:12:38.000Z",
  "updated": "2012-07-18T12:12:38.000Z",
  "title": "Critical exponents in zero dimensions",
  "authors": [
    "Alexandros Alexakis",
    "François Pétrélis"
  ],
  "categories": [
    "cond-mat.stat-mech",
    "nlin.CD",
    "physics.flu-dyn"
  ],
  "abstract": "In the vicinity of the onset of an instability, we investigate the effect of colored multiplicative noise on the scaling of the moments of the unstable mode amplitude. We introduce a family of zero dimensional models for which we can calculate the exact value of the critical exponents $\\beta_m$ for all the moments. The results are obtained through asymptotic expansions that use the distance to onset as a small parameter. The examined family displays a variety of behaviors of the critical exponents that includes anomalous exponents: exponents that differ from the deterministic (mean-field) prediction, and multiscaling: non-linear dependence of the exponents on the order of the moment.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-07-18T12:12:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "critical exponents",
      "zero dimensions",
      "zero dimensional models",
      "asymptotic expansions",
      "exact value"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s10955-012-0615-6",
      "journal": "Journal of Statistical Physics",
      "year": 2012,
      "month": "Nov",
      "volume": 149,
      "number": 4,
      "pages": 738
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012JSP...149..738A"
    }
  }
}