{
  "id": "cond-mat/0507424",
  "version": "v1",
  "published": "2005-07-18T20:54:46.000Z",
  "updated": "2005-07-18T20:54:46.000Z",
  "title": "Temperature dependent fluctuations in the two-dimensional XY model",
  "authors": [
    "S. T. Banks",
    "S. T. Bramwell"
  ],
  "comment": "15 pages, 5 figures and 1 table",
  "journal": "J. Phys. A: Math. Gen. 38, 5603 (2005)",
  "doi": "10.1088/0305-4470/38/25/001",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We present a detailed investigation of the probability density function (PDF) of order parameter fluctuations in the finite two-dimensional XY (2dXY) model. In the low temperature critical phase of this model, the PDF approaches a universal non-Gaussian limit distribution in the limit T-->0. Our analysis resolves the question of temperature dependence of the PDF in this regime, for which conflicting results have been reported. We show analytically that a weak temperature dependence results from the inclusion of multiple loop graphs in a previously-derived graphical expansion. This is confirmed by numerical simulations on two controlled approximations to the 2dXY model: the Harmonic and ``Harmonic XY'' models. The Harmonic model has no Kosterlitz-Thouless-Berezinskii (KTB) transition and the PDF becomes progressively less skewed with increasing temperature until it closely approximates a Gaussian function above T ~ 4\\pi. Near to that temperature we find some evidence of a phase transition, although our observations appear to exclude a thermodynamic singularity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-07-18T20:54:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "temperature dependent fluctuations",
      "two-dimensional xy model",
      "weak temperature dependence results",
      "universal non-gaussian limit distribution",
      "order parameter fluctuations"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2005,
      "month": "Jun",
      "volume": 38,
      "number": 25,
      "pages": 5603
    },
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005JPhA...38.5603B"
    }
  }
}