Stretched exponential relaxation in systems with random free energies

Abstract

A spin glass phase is characterized by a large number of quasi degenerate states (or walley bottoms). Their free energies F a =F o +f a , where f a is a non extensive fluctuation, have recently been shown to be random independent variables, as in Derrida's model. Relaxation to equilibrium of such systems is considered and a simple approximation to the transition probability (in the master equation) is considered that leads to a (random) relaxation time τ∼expβΔF with −β(F o +ΔF)= In a Σexp(−βF a ). The ensuing relaxation to equilibrium is shown to be a stretched exponential a behaviour common to a wide class of materials. The dependence of the result on the particular choice of the transition probability is touched upon Etude des verres de spin, caracterises par un grand nombre d'etats (ou fonds de vallees) quasi degeneres, d'energies libres F a =F o +f a (ou fa est une fluctuation non extensive) se comportant en variables aleatoires independantes comme dans le modele de Derrida. Analyse de la relaxation vers l'equilibre a l'aide d'une approximation simple pour la probabilite de transition (dans l'equation maitresse) qui conduit a un temps de relaxation aleatoire τ∼exp βΔF[F o +ΔF)=log a Σexp(−βF a )