Fisher renormalization for logarithmic corrections

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    Abstract

    For continuous phase transitions characterized by power-law divergences, Fisher renormalization prescribes how to obtain the critical exponents for a system under constraint from their ideal counterparts. In statistical mechanics, such ideal behaviour at phase transitions is frequently modified by multiplicative logarithmic corrections. Here, Fisher renormalization for the exponents of these logarithms is developed in a general manner. As for the leading exponents, Fisher renormalization at the logarithmic level is seen to be involutory and the renormalized exponents obey the same scaling relations as their ideal analogues. The scheme is tested in lattice animals and the Yang–Lee problem at their upper critical dimensions, where predictions for logarithmic corrections are made.
    Original languageEnglish
    Article numberL10002
    JournalJournal of Statistical Mechanics: Theory and Experiment
    Volume2008
    DOIs
    Publication statusPublished - 31 Oct 2008

    Bibliographical note

    The full text is also available from: http://de.arxiv.org/abs/0810.2719
    This is an author-created, un-copyedited version of an article accepted for publication/published in Journal of Statistical Mechanics: Theory and Experiment. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://dx.doi.org/10.1088/1742-5468/2008/10/L10002.

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