The Kosterlitz-Thouless universality class

Ralph Kenna, A. C. Irving

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    We examine the Kosterlitz-Thouless universality class and show that essential scaling at this type of phase transition is not self-consistent unless multiplicative logarithmic corrections are included. In the case of specific heat these logarithmic corrections are identified analytically. To identify those corresponding to the susceptibility we set up a numerical method involving the finite-size scaling of Lee-Yang zeroes. We also study the density of zeroes and introduce a new concept called index scaling. We apply the method to the XY model and the c]osely related step model in two dimensions. The critical parameters (including logarithmic corrections) of the step model are compatible with those of the XY model indicating that both models belong to the same universality class. This result then raises questions over how a vortex binding scenario can be the driving mechanism for the phase transition. Furthermore, the logarithmic corrections identified numerically by our methods of fitting are not in agreement with the renormalization group predictions of Kosterlitz and Thouless.
    Original languageEnglish
    Pages (from-to)583–612
    JournalNuclear Physics B
    Issue number3
    Publication statusPublished - 10 Feb 1997

    Bibliographical note

    The full text is also available from:
    NOTICE: this is the author’s version of a work that was accepted for publication in Nuclear Physics B. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Nuclear Physics B, [485, 3, 1997] DOI 10.1016/S0550-3213(96)00642-6.
    © 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International


    • Kosterlitz-Thouless
    • XY model
    • Logarithmic corrections
    • Lee-Yang zeroes
    • Finite-size scaling
    • Index scaling


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