Aging and domain growth in the two--dimensional Ising spin glass model

TL;DR

This study investigates aging and domain growth in the 2D Ising spin glass model using Monte Carlo simulations, revealing algebraic or logarithmic growth behaviors of domain sizes and autocorrelation functions.

Contribution

It provides the first detailed analysis of aging dynamics and domain growth laws in the 2D Ising spin glass with Gaussian couplings.

Findings

Aging is interrupted and characterized by specific scaling functions.

Domain size growth is compatible with algebraic or logarithmic laws.

Autocorrelation functions scale with waiting time and observation time.

Abstract

Interrupted aging in the two-dimensional Ising spin glass model with Gaussian couplings is established and investigated via extensive Monte-Carlo simulations. The spin autocorrelation function scales with $t/\tau(t_w)$, where $t_w$ is the waiting time and $\tau$ is equal to $t_w$ for waiting times smaller than the equilibration time $\tau_{\rm eq}$. The spatial correlations scale with $r/\xi(t_w)$, where the correlation length $\xi$ gives information about the averaged domain size in the system. Our results are better compatible with an algebraic growth law for $\xi(t_w)$, although it can also nicely be fitted to $(\log t_w)^{1/\psi}$ with $\psi\approx0.63$.