Numerical Study on Aging Dynamics in the 3D Ising Spin-Glass Model --- Quasi-Equilibrium Behaviour of Spin Auto-Correlation Functions

TL;DR

This study uses Monte Carlo simulations to analyze aging and quasi-equilibrium behaviors of spin auto-correlations in a 3D Ising spin-glass model, revealing scaling behaviors and weak violations of time invariance.

Contribution

It provides new insights into aging dynamics and quasi-equilibrium properties of 3D Ising spin glasses through detailed simulation analysis.

Findings

Scaling behavior observed in auto-correlation functions

Weak violation of time translational invariance

Growth laws show pre-asymptotic behavior

Abstract

Using Monte Carlo simulations, we have studied aging phenomena in three-dimensional Gaussian Ising spin-glass model focusing on quasi-equilibrium behavior of the spin auto-correlation functions. 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. The simulated results in not only isothermal but also $T$-shift aging processes exhibit the expected scaling behavior with respect to the characteristic length scales associated with droplet excitations and domain walls in spite of the fact that the growth law for these length scales still shows a pre-asymptotic behavior compared with the asymptotic form proposed by the droplet theory. Implications of our simulational results are also discussed in relation to experimental observations.