RELAXATION AND AGING IN SPIN-GLASSES AND OTHER COMPLEX-SYSTEMS

We describe how a hierachical model of spin glass relaxation can display aging behaviour, similarly to what is found in spin glasses and other complex systems out of thermodynamic equilibrium. Since we deal with a nonequilibrium situation, the usual F(luctuation)D(issipation)T(heory) does not apply. We therefore derive a general relation between the linear response function and the non equilibrium propagator of the unperturbed system. The relation is shown to be very similar to the equilibrium FDT under certain conditions, which one can reasonably assume for spin glass systems. Having thus related the linear response of the system to a small external field to the autocorrelation function of the magnetization, we calculate the latter quantity by a master equation on a set of states which have the topology of a tree. The model can reproduce the main qualitative features of the Z(ero)F(ield)C(ooled) spin glass experiments, i.e. the maximum in the logarithmic time derivative of the magnetization, with only two free parameters. © 1990 Springer-Verlag.