{
  "id": "1102.4149",
  "version": "v3",
  "published": "2011-02-21T07:08:11.000Z",
  "updated": "2011-11-18T16:59:31.000Z",
  "title": "Bayesian Inference in the Scaling Analysis of Critical Phenomena",
  "authors": [
    "Kenji Harada"
  ],
  "comment": "7 pages, 8 figures, and 1 table",
  "journal": "Phys. Rev. E 84, 056704 (2011)",
  "doi": "10.1103/PhysRevE.84.056704",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.str-el",
    "physics.comp-ph",
    "physics.data-an"
  ],
  "abstract": "To determine the universality class of critical phenomena, we propose a method of statistical inference in the scaling analysis of critical phenomena. The method is based on Bayesian statistics, most specifically, the Gaussian process regression. It assumes only the smoothness of a scaling function, and it does not need a form. We demonstrate this method for the finite-size scaling analysis of the Ising models on square and triangular lattices. Near the critical point, the method is comparable in accuracy to the least-square method. In addition, it works well for data to which we cannot apply the least-square method with a polynomial of low degree. By comparing the data on triangular lattices with the scaling function inferred from the data on square lattices, we confirm the universality of the finite-size scaling function of the two-dimensional Ising model.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-11-18T16:59:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.10.-a",
      "64.60.F-",
      "02.50.Tt"
    ],
    "keywords": [
      "scaling analysis",
      "critical phenomena",
      "bayesian inference",
      "scaling function",
      "triangular lattices"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "year": 2011,
      "month": "Nov",
      "volume": 84,
      "number": 5,
      "pages": "056704"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011PhRvE..84e6704H"
    }
  }
}