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 and the growth of correlations is observed. The spatial decay of the correlations at distances less than the dynamic correlation length 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 and find that it is compatible with the mean-field value of the critical dynamical exponent for short range spin glasses.