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

The low-temperature dynamics of the two- and 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,t(w))=[[S-i(t+t(w))S-i(t(w))]](av) a typical aging scenario with a t/t(w), scaling is established. Investigating spatial correlations we find an algebraic growth law xi(t(w))similar to t(w)(alpha(T)) of the average domain size. The spatial correlation function G(r,t(w))=[[S-i(t(w))S-i+r(t(w))](2)](av) scales with r/xi(t(w)). 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 100 x 100) and then we calculate the correlations between this state and the states generated during a Monte Carlo simulation.