Distribution of local Lyapunov exponents in spin-glass dynamics

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dc.creatorde Queiroz, S. L. A
dc.creatorStinchcombe, R. B.
dc.date2007-03-16
dc.date2007-10-29
dc.date.accessioned2026-07-07T08:43:14Z
dc.date.available2026-07-07T08:43:14Z
dc.descriptionWe investigate the statistical properties of local Lyapunov exponents which characterize magnon localization in the $d=1$ Heisenberg-Mattis spin glass (HMSG) at zero temperature, by means of a connection to a suitable version of the Fokker-Planck (F-P) equation. We consider the local Lyapunov exponents (LLE), in particular the case of {\em instantaneous} LLE. We establish a connection between the transfer-matrix recursion relation for the problem, and an F-P equation governing the evolution of the probability distribution of the instantaneous LLE. The closed-form (stationary) solutions to the F-P equation are in excellent accord with numerical simulations, for both the unmagnetized and magnetized versions of the HMSG. Scaling properties for non-stationary conditions are derived from the F-P equation in a special limit (in which diffusive effects tend to vanish), and also shown to provide a close description to the corresponding numerical-simulation data.
dc.descriptionFinal version, to be published in Phys. Rev. B
dc.identifierhttps://arxiv.org/abs/cond-mat/0703444
dc.identifierhttp://arxiv.org/abs/cond-mat/0703444
dc.identifierPhysical Review B 76,184421 (2007)
dc.identifierdoi:10.1103/PhysRevB.76.184421
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/142246
dc.subjectStatistical Mechanics
dc.subjectDisordered Systems and Neural Networks
dc.titleDistribution of local Lyapunov exponents in spin-glass dynamics
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