Evidence of the de Almeida-Thouless transition in three-dimensional spin glasses

TL;DR

This study introduces a new computational method to detect the de Almeida-Thouless transition in three-dimensional spin glasses, providing numerical evidence supporting the existence of a phase transition in these systems.

Contribution

A novel robust approach to define spin-glass susceptibility was developed, enabling clear identification of the de Almeida-Thouless transition in 3D spin glasses.

Findings

Susceptibility peaks diverge with system size in 3D spin glasses under a field.

The susceptibility behavior indicates a phase transition consistent with replica symmetry breaking.

Contrasts with 2D and mean-field models highlight the unique nature of the 3D dAT transition.

Abstract

The nature of spin-glass states in a magnetic field remains a major open problem in statistical physics. The existence of the de Almeida-Thouless (dAT) transition for three-dimensional (3D) spin glasses in a field is still debated. We introduce a new computational method to define the spin-glass susceptibility, which is robust against the broad tail in the overlap distribution that undermines conventional analyses. Applying this approach to the Edwards-Anderson spin-glass model in 2D and 3D, and contrasting with the 3D Ising (without disorder) and mean-field spin-glass models, we find a stark difference: the locus of susceptibility maxima bends to the right in the field-temperature plane for the Ising and 2D spin-glass cases, indicating a supercritical crossover line, but bends to the left for the mean-field and 3D spin glasses - a signature of the dAT line. Finite-size scaling further suggests that the peak susceptibility diverges with system size in 3D spin glasses under a field, while saturating in 2D. These results provide direct numerical evidence for the dAT transition in 3D, supporting the replica symmetry breaking scenario.