Spin glass overlap barriers in three and four dimensions

TL;DR

This study uses high-statistics Monte Carlo simulations to analyze free-energy barriers in 3D and 4D spin glasses, revealing non-self-averaging behavior and the dominance of hidden barriers in autocorrelation times.

Contribution

It provides the first detailed analysis of free-energy barriers in 3D and 4D spin glasses using the multi-overlap algorithm, highlighting their non-self-averaging nature.

Findings

Barriers are non-self-averaging in both dimensions.

Hidden barriers in q dominate autocorrelation times.

Autocorrelation times are influenced by barriers not visible in P_J(q).

Abstract

For the Edwards-Anderson Ising spin-glass model in three and four dimensions (3d and 4d) we have performed high statistics Monte Carlo calculations of those free-energy barriers $F^q_B$ which are visible in the probability density $P_J(q)$ of the Parisi overlap parameter $q$. The calculations rely on the recently introduced multi-overlap algorithm. In both dimensions, within the limits of lattice sizes investigated, these barriers are found to be non-self-averaging and the same is true for the autocorrelation times of our algorithm. Further, we present evidence that barriers hidden in $q$ dominate the canonical autocorrelation times.