Ising Spin Glasses in a Magnetic Field

TL;DR

This paper investigates the stability of the spin glass phase in three-dimensional Edwards-Anderson models under an external magnetic field, finding that the phase does not survive any finite field, supporting the droplet model over mean field theory.

Contribution

The study provides the first large-scale computational analysis of ground states in 3D spin glasses with magnetic fields, confirming theoretical predictions about phase stability.

Findings

Spin glass phase vanishes at any finite magnetic field.

Supports droplet model predictions over mean field theory.

Analyzed systems with up to 600 spins.

Abstract

Ground states of the three dimensional Edwards-Anderson spin glass are computed in the presence of an external magnetic field. Our algorithm is sufficiently powerful for us to treat systems with up to 600 spins. We perform a statistical analysis of how the ground state changes as the field is increased, and reach the conclusion that the spin glass phase at zero temperature does not survive in the presence of any finite field. This is in agreement with the droplet model or scaling predictions, but in sharp disagreement with the mean field picture. For comparison, we also investigate a dilute mean field spin glass model where an Almeida-Thouless line is present.