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

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dc.creatorMilovanov, Alexander V.
dc.creatorRasmussen, Jens J.
dc.date2003-09-25
dc.date2004-07-22
dc.date.accessioned2026-07-07T02:53:46Z
dc.date.available2026-07-07T02:53:46Z
dc.descriptionEquations 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.
dc.description10 pages, improved content, submitted for publication to Phys. Lett. A
dc.identifierhttps://arxiv.org/abs/cond-mat/0309577
dc.identifierhttp://arxiv.org/abs/cond-mat/0309577
dc.identifierPhysics Letters A 337 (2005) 75-80
dc.identifierdoi:10.1016/j.physleta.2005.01.047
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/22291
dc.subjectSuperconductivity
dc.titleFractional generalization of the Ginzburg-Landau equation: An unconventional approach to critical phenomena in complex media
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