Off-equilibrium dynamics in finite-dimensional spin-glass models.

The low-temperature dynamics of the twoand three-dimensional Ising spin-glass model with Gaussian couplings is investigated via extensive Monte Carlo simulations. We find an algebraic decay of the remanent magnetization. For the autocorrelation function C(t ,tw)5@^Si(t1tw)Si(tw)&#av a typical aging scenario with a t/tw scaling is established. Investigating spatial correlations we find an algebraic growth law j(tw);tw a(T) of the average domain size. The spatial correlation function G(r ,tw)5@^Si(tw)Si1r(tw)& #av scales with r/j(tw). The sensitivity of the correlations in the spin-glass phase with respect to temperature changes is examined by calculating a time-dependent overlap length. In the two-dimensional model we examine domain growth with the following method: first we determine the exact ground states of the various samples ~of system sizes up to 1003100) and then we calculate the correlations between this state and the states generated during a Monte Carlo simulation.