Fractional generalization of the Ginzburg–Landau equation: an unconventional approach to critical phenomena in complex media

A.V. Milovanov, J. Juul Rasmussen

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    Abstract

    Equations built on fractional derivatives prove to be a powerful tool in the description of complex systems when the effects of singularity, fractal supports, and long-range dependence play a role. In this Letter, we advocate an application of the fractional derivative formalism to a fairly general class of critical phenomena when the organization of the system near the phase transition point is influenced by a competing nonlocal ordering. Fractional modifications of the free energy functional at criticality and of the widely known Ginzburg-Landau equation central to the classical Landau theory of second-type phase transitions are discussed in some detail. An implication of the fractional Ginzburg-Landau equation is a renormalization of the transition temperature owing to the nonlocality present. (c) 2005 Elsevier B.V. All rights reserved.
    Original languageEnglish
    JournalPhysics Letters A
    Volume337
    Issue number1-2
    Pages (from-to)75-80
    ISSN0375-9601
    DOIs
    Publication statusPublished - 2005

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