Reply to Comment on "Ising Spin Glasses in a Magnetic Field"

TL;DR

This paper discusses the debate over the existence of a spin glass phase in a magnetic field, emphasizing the limitations of dynamic methods and reanalyzing data to suggest larger system sizes are needed for conclusive results.

Contribution

The authors critique dynamic approaches for detecting the Almeida-Thouless line and reanalyze data indicating the necessity of larger lattice sizes for finite size scaling.

Findings

Dynamic methods may not reliably detect the Almeida-Thouless line.

Finite size scaling requires lattice sizes around 20x20x20 for small fields.

Results suggest the critical field near B=0.4 at zero temperature.

Abstract

The problem of the survival of a spin glass phase in the presence of a field has been a challenging one for a long time. To date, all attempts using equilibrium Monte Carlo methods have been unconclusive. In their comment to our paper, Marinari, Parisi and Zuliani use out-of-equilibrium measurements to test for an Almeida-Thouless line. In our view such a dynamic approach is not based on very solid foundations in finite dimensional systems and so cannot be as compelling as equilibrium approaches. Nevertheless, the results of those authors suggests that there is a critical field near B=0.4 at zero temperature. In view of this quite small value (compared to the mean field value), we have reanalyzed our data. We find that if finite size scaling is to distinguish between that small field and a zero field, we would need to go to lattice sizes of about 20x20x20.