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

TL;DR

This study uses Monte Carlo simulations to analyze the aging behavior of the 3D Ising spin-glass model, focusing on the quasi-equilibrium regime of the spin auto-correlation function and its scaling properties.

Contribution

It provides new insights into the scaling behavior of effective stiffness and droplet excitations during aging in the 3D Ising spin-glass model, linking simulation results to experimental observations.

Findings

Effective stiffness follows expected scaling with droplet size.

Growth law of domain walls extracted from simulations.

Weak violation of time translational invariance observed.

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 {\it 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.