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

Abstract

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, ℓT , such that length scales smaller that ℓT are equilibrated, whereas larger length scales are essentially frozen. The time and temperature dependence of ℓT 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' ψ which we estimate to be ψ ∼ 1.0 and ψ ∼ 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.

Rejuvenation and memory in model spin glasses in three and four dimensions

“…Yet, difficulties have arisen in numerical investigation of memory and rejuvenation. 9,[24][25][26][27] Furthermore, the progress achieved regards temperature-shift and temperature-cycle experiments. The dip-experiment protocol remains still as too complicated to be analyzed theoretically.…”

“…However, when it comes to actual calculations, it turns out that no convincing memory and rejuvenation has been found in computer simulations of three-dimensional ͑3D͒ spin-glass models, either with a two-temperature 9,24,26,27 or with a dip-experiment protocol. 25 When the behavior of the coherence length is followed for times up to 10 5 MCSs, 24 Eqs.…”

“…In this work, we report simulations of a 3D ͑made with the SUE machine 35 ͒ and a 4D EA model with binary ͑rather than Gaussian [24][25][26]34 ͒ couplings. Our 3D simulations are three orders of magnitude longer than previous ones.…”

“…Hence one assumes [24][25][26]34 to be in pseudoequilibrium regime ͑ t w ӷ 1 thus X͓C͔ =1͒, which is not always true. We also obtain spatial information from the correlation function of the overlap field, q i ͑t͒ = i ͑1͒ ͑t͒ i ͑2͒ ͑t͒, built from two independently evolving systems with the same couplings, at the same temperature:…”

“…The constant behavior of ␣ does not agree with the results for the 4D model with Gaussian couplings. 26 To estimate errors in the three-parameter fit ͑8͒ is very difficult. To have a feeling of their magnitude, let us report that ␣ = 0.7 yields good fits as well, with a 10% increased estimate.…”