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

Alexander V. Milovanov; Jens J. Rasmussen

doi:10.1016/j.physleta.2005.01.047

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

Alexander V. Milovanov·Jens J. 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 paper, 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.

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Alexander V. Milovanov, Jens J. Rasmussen. 2004-07-22. Fractional generalization of the Ginzburg-Landau equation: An unconventional approach to critical phenomena in complex media. https://doi.org/10.1016/j.physleta.2005.01.047

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