A domain theory for linear and nonlinear aging effects in spin glasses

Abstract

We present a theory of aging in spin glasses subjected to a time-dependent temperature and external magnetic field. An arbitrary nonequilibrium spin glass state is imagined to be decomposable into a collection of «(T 1 ,H 1 )-domains» (for any pair (T 1 ,H 1 )) through a comparison of this state to an equilibrium state at a temperature T 1 and in a field H 1 . The theory postulates a time evolution for the domains (comprising both growth and breakup), as well as an equation for the magnetic relaxation within a domain. Of crucial importance is the interplay between two characteristics lengths: i) the time-dependent linear size of a domain, and ii) an overlap length l (ΔT,ΔH); the latter indicates up until which length scale two thermodynamic equilibrium states differing by ΔT and ΔH are indistinguishable. We show that the theory explains a variety of experimental aging effects as have been observed in particular by Refregier et al. and by Lundgren et al. Theorie du vieillissement dans les verres de spin soumis a une temperature et un champ magnetique externe dependant du temps, basee sur l'hypothese qu'un etat de verre de spin arbitraire hors equilibre peut etre decompose en une collection de «domaines (T 1 ,H 1 )» par comparaison a un etat d'equilibre a une temperature T 1 dans un champ H 1 . Equations d'evolution decrivant la croissance et la fracturation des domaines, equation de relaxation magnetique a l'interieur d'un domaine. Role crucial de l'interaction de deux longueurs caracteristiques definissant la dimension lineaire d'un domaine et l'echelle d'indiscernabilite de deux etats d'equilibre thermodynamique differant par ΔT et ΔH. Interpretation satisfaisante d'une serie de resultats experimentaux