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,${\mathit{t}}_{\mathit{w}}$)=[〈${\mathit{S}}_{\mathit{i}}$(t+${\mathit{t}}_{\mathit{w}}$)${\mathit{S}}_{\mathit{i}}$(${\mathit{t}}_{\mathit{w}}$)〉${]}_{\mathrm{av}}$ a typical aging scenario with a t/${\mathit{t}}_{\mathit{w}}$ scaling is established. Investigating spatial correlations we find an algebraic growth law ξ(${\mathit{t}}_{\mathit{w}}$)∼${\mathit{t}}_{\mathit{w}}^{\mathrm{\alpha }\left(\mathit{T}\right)}$ of the average domain size. The spatial correlation function G(r,${\mathit{t}}_{\mathit{w}}$) =[〈${\mathit{S}}_{\mathit{i}}$(${\mathit{t}}_{\mathit{w}}$)${\mathit{S}}_{\mathit{i}+\mathit{r}}$(${\mathit{t}}_{\mathit{w}}$)${\mathrm{〉}}^2$ ${]}_{\mathrm{av}}$ scales with r/ξ(${\mathit{t}}_{\mathit{w}}$). 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.