Geometrical Aspects of Aging and Rejuvenation in the Ising Spin Glass: A Numerical Study

We present a comprehensive study of non-equilibrium phenomena in the low temperature phase of the Edwards-Anderson Gaussian spin glass in 3 and 4 spatial dimensions. Many effects can be understood in terms of a time dependent coherence length, ${\mathrm{\ell }}_T$, such that length scales smaller that ${\mathrm{\ell }}_T$ are equilibrated, whereas larger length scales are essentially frozen. The time and temperature dependence of ${\mathrm{\ell }}_T$ is found to be compatible with critical power-law dynamical scaling for small times/high temperatures, crossing over to an activated logarithmic growth for longer times/lower temperatures, in agreement with recent experimental results. The activated regime is governed by a barrier exponent' psi which we estimate to be psi ~ 1.0 and psi ~ 2.3 in 3 and 4 dimensions, respectively. We observe for the first time the rejuvenation and memory effects in the four dimensional sample, which, we argue, is unrelated to temperature chaos’. Our discussion in terms of length scales allows us to address several experimentally relevant issues, such as super-aging versus sub-aging effects, the role of a finite cooling rate, or the so-called Kovacs effect.