The Link Overlap and Finite Size Effects for the 3D Ising Spin Glass

TL;DR

This paper investigates the link overlap in 3D Ising spin glasses, showing that finite size effects and the droplet picture explain observed behaviors, challenging the replica symmetry breaking interpretation.

Contribution

It demonstrates that the droplet picture accounts for the link overlap distribution and finite size effects in 3D Ising spin glasses, contrasting with replica symmetry breaking.

Findings

Link overlap distribution shows asymmetry and sample-to-sample variations.

Scaling of the distribution width aligns with the droplet picture.

Asymptotic droplet behavior is unobservable at moderate sizes and temperatures.

Abstract

We study the link overlap between two replicas of an Ising spin glass in three dimensions using the Migdal-Kadanoff approximation and scaling arguments based on the droplet picture. For moderate system sizes, the distribution of the link overlap shows the asymmetric shape and large sample-to-sample variations found in Monte Carlo simulations and usually attributed to replica symmetry breaking. However, the scaling of the width of the distribution, and the link overlap in the presence of a weak coupling between the two replicas are in agreement with the droplet picture. We also discuss why it is impossible to see the asymptotic droplet-like behaviour for moderate system sizes and temperatures not too far below the critical temperature.