Off-Equilibrium Dynamics in Finite-Dimensional Spin Glass Models

TL;DR

This study uses extensive Monte Carlo simulations to analyze the off-equilibrium dynamics of 2D and 3D Ising spin glasses, revealing algebraic decay, aging behavior, domain growth, and sensitivity to temperature changes.

Contribution

It provides new insights into off-equilibrium dynamics of finite-dimensional spin glasses, including a novel method for examining domain growth in 2D models using ground state comparisons.

Findings

Algebraic decay of remanent magnetization

Aging with t/t_w scaling in autocorrelation functions

Algebraic growth law of domain size with t_w

Abstract

The low temperature dynamics of the two- and three-dimensional Ising spin glass model with Gaussian couplings is investigated via extensive Monte Carlo simulations. We find an algebraic decay of the remanent magnetization. For the autocorrelation function $C(t,t_w)=[< S_i(t+t_w)S_i(t_w)>]_{av}$ a typical aging scenario with a $t/t_w$ scaling is established. Investigating spatial correlations we find an algebraic growth law $\xi(t_w)\sim t_w^{\alpha(T)}$ of the average domain size. The spatial correlation function $G(r,t_w)=[< S_i(t_w)S_{i+r}(t_w)>^2]_{av}$ scales with $r/\xi(t_w)$. The sensitivity of the correlations in the spin glass phase with respect to temperature changes is examined by calculating a time dependent overlap length. In the two dimensional model we examine domain growth with a new method: First we determine the exact ground states of the various samples (of system sizes up to $100\times 100$) and then we calculate the correlations between this state and the states generated during a Monte Carlo simulation.