Study of the de Almeida-Thouless line using power-law diluted one-dimensional Ising spin glasses

TL;DR

This study uses Monte Carlo simulations to investigate the existence of the de Almeida-Thouless line in a one-dimensional Ising spin glass with power-law interactions, finding it only exists in the mean field regime (dimension > 6).

Contribution

It provides numerical evidence that the Almeida-Thouless line appears only in the mean field regime for power-law diluted one-dimensional Ising spin glasses.

Findings

Almeida-Thouless line exists only in the mean field regime.

No evidence of the line in lower dimensions.

Supports the theoretical prediction for high-dimensional spin glasses.

Abstract

We test for the existence of a spin-glass phase transition, the de Almeida-Thouless line, in an externally-applied (random) magnetic field by performing Monte Carlo simulations on a power-law diluted one-dimensional Ising spin glass for very large system sizes. We find that an Almeida-Thouless line only occurs in the mean field regime, which corresponds, for a short-range spin glass, to dimension d larger than 6.