Interface Energy in the Edwards-Anderson model

TL;DR

This paper numerically investigates the energy cost of interface changes in 3D spin glasses, providing evidence for a lower critical dimension around 2.5 and aligning with mean field theory predictions.

Contribution

It introduces a numerical approach to analyze interface energy in the Edwards-Anderson model at finite temperatures, supporting the lower critical dimension estimate.

Findings

Lower critical dimension estimated at 2.5

Results agree with mean field theory predictions

Method applicable to finite temperature spin glass systems

Abstract

We numerically investigate the spin glass energy interface problem in three dimensions. We analyze the energy cost of changing the overlap from -1 to +1 at one boundary of two coupled systems (in the other boundary the overlap is kept fixed to +1). We implement a parallel tempering algorithm that simulate finite temperature systems and work with both cubic lattices and parallelepiped with fixed aspect ratio. We find results consistent with a lower critical dimension $D_c=2.5$. The results show a good agreement with the mean field theory predictions.