Numerical Study on Aging Dynamics in the 3D Ising Spin-Glass Model. II. Quasi-Equilibrium Regime of Spin Auto-Correlation Function

Abstract

Using Monte Carlo simulations, we have studied isothermal aging of three-dimensional Ising spin-glass model focusing on quasi-equilibrium behavior of the spin auto-correlation function. Weak violation of the time translational invariance in the quasi-equilibrium regime is analyzed in terms of effective stiffness for droplet excitations in the presence of domain walls. Within the range of computational time window, we have confirmed that the effective stiffness follows the expected scaling behavior with respect to the characteristic length scales associated with droplet excitations and domain walls, whose growth law has been extracted from our simulated data. Implication of the results are discussed in relation to experimental works on ac susceptibilities.

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

“…A nice exception is the simulations of Ref. 24 eff,shift ͒ when the measured effective times are converted in length scales, both for T 2 Ͼ T 1 and T 1 Ͻ T 2 , in contradiction with Eq. ͑4͒.…”

“…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.…”

“…25 When the behavior of the coherence length is followed for times up to 10 5 MCSs, 24 Eqs. ͑4͒ and ͑5͒ are fulfilled even for ͑T 1 − T 2 ͒ / T 2 Ϸ ± 0.33.…”

“…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:…”