{
  "id": "1104.0432",
  "version": "v2",
  "published": "2011-04-03T22:36:35.000Z",
  "updated": "2011-07-09T00:48:18.000Z",
  "title": "Finite-size scaling from self-consistent theory of localization",
  "authors": [
    "I. M. Suslov"
  ],
  "comment": "Latex, 23 pages, figures included; additional Fig.8 is added with high precision data by Kramer et al",
  "journal": "J.Exp.Theor.Phys. 114, 107-117 (2012) [Zh.Eksp.Teor.Fiz. 141, 122-134 (2012) ]",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech"
  ],
  "abstract": "Accepting validity of self-consistent theory of localization by Vollhardt and Woelfle, we derive the finite-size scaling procedure used for studies of the critical behavior in d-dimensional case and based on the use of auxiliary quasi-1D systems. The obtained scaling functions for d=2 and d=3 are in good agreement with numerical results: it signifies the absence of essential contradictions with the Vollhardt and Woelfle theory on the level of raw data. The results \\nu=1.3-1.6, usually obtained at d=3 for the critical exponent of the correlation length, are explained by the fact that dependence L+L_0 with L_0>0 (L is the transversal size of the system) is interpreted as L^{1/\\nu} with \\nu>1. For dimensions d\\ge 4, the modified scaling relations are derived; it demonstrates incorrectness of the conventional treatment of data for d=4 and d=5, but establishes the constructive procedure for such a treatment. Consequences for other variants of finite-size scaling are discussed.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-07-09T00:48:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "self-consistent theory",
      "finite-size scaling",
      "localization",
      "auxiliary quasi-1d systems",
      "d-dimensional case"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1134/S1063776111150131",
      "journal": "Soviet Journal of Experimental and Theoretical Physics",
      "year": 2012,
      "month": "Jan",
      "volume": 114,
      "number": 1,
      "pages": 107
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012JETP..114..107S"
    }
  }
}