Interfaces and Lower Critical Dimension in a Spin Glass Model

TL;DR

This paper estimates the lower critical dimension for replica symmetry breaking in spin glasses by calculating the free-energy cost of domain walls, suggesting a critical dimension of 2.5.

Contribution

It introduces a method to estimate the lower critical dimension in spin glasses based on domain wall free-energy calculations, providing a new perspective.

Findings

Lower critical dimension estimated at 2.5

Domain wall free-energy analysis applied to spin glasses

Implications for replica symmetry breaking

Abstract

In this paper we try to estimate the lower critical dimension for replica symmetry breaking in spin glasses through the calculation of the additional free-energy required to create a domain wall between two different phases. This mechanism alone would say that replica symmetry would be restored at the lower critical dimension $D_c =2.5$.