Geometrical aspects of aging and rejuvenation in the Ising spin glass: A numerical study

We present a comprehensive study of nonequilibrium phenomena in the low-temperature phase of the Edwards-Anderson Gaussian spin glass in three and four spatial dimensions. Many effects can be understood in terms of a time-dependent coherence length $l_T$ such that length scales smaller than $l_T$ are equilibrated, whereas larger length scales are essentially frozen. The time and temperature dependences of $l_T$ are found to be compatible with critical power-law dynamical scaling for small times and high temperatures, crossing over to an activated logarithmic growth for longer times and lower temperatures, in agreement with recent experimental results. The activated regime is governed by a “barrier exponent” $\psi$ which we estimate to be $\psi \sim 1.0$ and 2.3 in three and four dimensions, respectively. We observe 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 superaging versus subaging effects, the role of a finite cooling rate, or the so-called Kovacs effect.