The connection between statics and dynamics of spin glasses

We present results of numerical simulations on a one-dimensional Ising spin glass with long-range interactions. Parameters of the model are chosen such that it is a proxy for a short-range spin glass above the upper critical dimension (i.e. in the mean-field regime). The system is quenched to a temperature well below the transition temperature T-c and the growth of correlations is observed. The spatial decay of the correlations at distances less than the dynamic correlation length xi(t) agrees quantitatively with the predictions of a static theory, the 'metastate', evaluated according to the replica symmetry breaking (RSB) theory. We also compute the dynamic exponent z(T) defined by xi(t) alpha t(1/z(T)) and find that it is compatible with the mean-field value of the critical dynamical exponent for short range spin glasses.