Evidence for the droplet/scaling picture of spin glasses

TL;DR

This paper investigates the behavior of the Parisi overlap distribution in 3D Ising spin glasses, showing evidence for replica symmetry breaking near the transition and droplet scaling at lower temperatures, highlighting the importance of system size and temperature in simulations.

Contribution

It provides evidence supporting the droplet/scaling picture at low temperatures using the Migdal-Kadanoff approximation, contrasting with previous Monte Carlo results.

Findings

At T ≈ 0.7Tc, P(q) matches replica symmetry breaking predictions.

At lower T, data align with droplet or scaling models.

System size and temperature proximity to Tc affect observed behavior.

Abstract

We have studied the Parisi overlap distribution for the three dimensional Ising spin glass in the Migdal-Kadanoff approximation. For temperatures T around 0.7Tc and system sizes upto L=32, we found a P(q) as expected for the full Parisi replica symmetry breaking, just as was also observed in recent Monte Carlo simulations on a cubic lattice. However, for lower temperatures our data agree with predictions from the droplet or scaling picture. The failure to see droplet model behaviour in Monte Carlo simulations is due to the fact that all existing simulations have been done at temperatures too close to the transition temperature so that sytem sizes larger than the correlation length have not been achieved.