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,tw)=[〈Sᵢ(t+tw)Sᵢ(tw)〉]ₐᵥ a typical aging scenario with a t/tw scaling is established. Investigating spatial correlations we find an algebraic growth law {ξ}(tw){~}tw^α(T) of the average domain size. The spatial correlation function G(r,tw) =[〈Sᵢ(tw)Sᵢ₊ᵣ(tw)〉²{]}ₐᵥscales with r/ξ({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×{}100) and then we calculate the correlations between this state and the states generated during a Monte Carlo simulation. {} 1996 The American Physical Society.