Correlations between the dynamics of parallel tempering and the free-energy landscape in spin glasses

TL;DR

This study uses large-scale simulations to analyze how the free-energy landscape's complexity influences the dynamics of parallel tempering in 3D spin glasses, revealing a direct correlation between landscape roughness and autocorrelation times.

Contribution

It provides the first comprehensive numerical analysis linking free-energy landscape features with dynamic behavior in 3D spin glasses using parallel tempering.

Findings

Autocorrelation times increase with landscape roughness.

Static and dynamic observables are strongly correlated.

Results hold for large disorder samples and low temperatures.

Abstract

We present the results of a large-scale numerical study of the equilibrium three-dimensional Edwards-Anderson Ising spin glass with Gaussian disorder. Using parallel tempering (replica exchange) Monte Carlo we measure various static, as well as dynamical quantities, such as the autocorrelation times and round-trip times for the parallel tempering Monte Carlo method. The correlation between static and dynamic observables for 5000 disorder realizations and up to 1000 spins down to temperatures at 20% of the critical temperature is examined. Our results show that autocorrelation times are directly correlated with the roughness of the free-energy landscape.