Dynamic Variational Study of Chaos: Spin Glasses in Three Dimensions

TL;DR

This paper introduces a variational method to better estimate correlation times in Parallel Tempering dynamics, enabling a refined analysis of temperature chaos in three-dimensional spin glasses and revealing fat-tailed, finite-size scaling distributions.

Contribution

It presents a novel variational approach to compute correlation times, improving the understanding of chaos phenomena in finite-dimensional spin glasses.

Findings

Correlation times have fat-tailed distributions.

Finite-size scaling applies to the distribution of characteristic times.

The variational method provides a lower bound estimate of exponential correlation times.

Abstract

We have introduced a variational method to improve the computation of integrated correlation times in the Parallel Tempering Dynamics, obtaining a better estimate (a lower bound, at least) of the exponential correlation time. Using this determination of the correlation times, we revisited the problem of the characterization of the chaos in temperature in finite dimensional spin glasses by means of the study of correlations between different chaos indicators computed in the static and the correlation times of the Parallel Tempering dynamics. The sample-distribution of the characteristic time for the Parallel Tempering dynamics turns out to be fat-tailed and it obeys finite-size scaling.