Non-equilibrium dynamics in the random bond Ising chain: A reminiscence of aging in spin glasses

TL;DR

This paper uses Monte Carlo simulations to explore the aging and out-of-equilibrium behavior of a one-dimensional Gaussian bond Ising spin glass, revealing simple scaling laws in correlations and domain growth.

Contribution

It provides detailed analysis of spatial correlations and domain statistics, highlighting aging phenomena in a 1D spin glass model with new insights into scaling behaviors.

Findings

Aging scenario observed at low temperatures similar to higher-dimensional models

Correlation functions and domain-size distributions follow simple scaling laws

Slow domain growth underpins the out-of-equilibrium dynamics

Abstract

Results of extensive Monte-Carlo simulations that investigate the out-of-equilibrium dynamics of the one-dimensional Ising spin glass model with a Gaussian bond-distribution are presented. At low enough temperatures a typical (interrupted) aging scenario is established as in two- and similar to three-dimensional spin glass models. Since the underlying mechanism is a slow domain-growth we study in detail spatial correlations and the time-dependence of the domain- as well as kink-statistics. We find that all correlation functions in time and in space as well as the domain-size probability distribution function obey simple scaling laws.