On Equilibrium Dynamics of Spin-Glass Systems

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dc.creatorCrisanti, A.
dc.creatorLeuzzi, L.
dc.date2006-06-15
dc.date2006-11-21
dc.date.accessioned2026-07-07T07:56:35Z
dc.date.available2026-07-07T07:56:35Z
dc.descriptionWe present a critical analysis of the Sompolinsky theory of equilibrium dynamics. By using the spherical $2+p$ spin glass model we test the asymptotic static limit of the Sompolinsky solution showing that it fails to yield a thermodynamically stable solution. We then present an alternative formulation, based on the Crisanti, Hörner and Sommers [Z. für Physik {\bf 92}, 257 (1993)] dynamical solution of the spherical $p$-spin spin glass model, reproducing a stable static limit that coincides, in the case of a one step Replica Symmetry Breaking Ansatz, with the solution at the dynamic free energy threshold at which the relaxing system gets stuck off-equilibrium. We formally extend our analysis to any number of Replica Symmetry Breakings $R$. In the limit $R\to\infty$ both formulations lead to the Parisi anti-parabolic differential equation. This is the special case, though, where no dynamic blocking threshold occurs. The new formulation does not contain the additional order parameter $Δ$ of the Sompolinsky theory.
dc.description24 pages, 6 figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0606425
dc.identifierhttp://arxiv.org/abs/cond-mat/0606425
dc.identifierPhys. Rev. B 75, 144301 (2007)
dc.identifierdoi:10.1103/PhysRevB.75.144301
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/127361
dc.subjectDisordered Systems and Neural Networks
dc.subjectStatistical Mechanics
dc.titleOn Equilibrium Dynamics of Spin-Glass Systems
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