Spin glasses in a field: Three and four dimensions as seen from one space dimension

TL;DR

This study investigates the existence of the de Almeida-Thouless line in spin glasses across three and four dimensions using one-dimensional models with power-law interactions, employing advanced finite-size scaling methods.

Contribution

It applies a novel finite-size scaling approach to spin glass models to analyze the de Almeida-Thouless line in different dimensions, highlighting discrepancies and challenges.

Findings

No evidence of the de Almeida-Thouless line in three dimensions.

Conflicting results between new and traditional scaling in four dimensions.

Highlights the need for improved finite-size scaling techniques.

Abstract

We study the existence of a line of transitions of an Ising spin glass in a magnetic field-known as the de Almeida-Thouless line-using one-dimensional power-law diluted Ising spin-glass models. We choose the power-law exponent to have values that approximately correspond to three- and four-dimensional nearest-neighbor systems and perform a detailed finite-size scaling analysis of the data for large linear system sizes, both using a new approach proposed recently [Phys. Rev. Lett. 103, 267201 (2009)], as well as traditional approaches. Our results for the model corresponding to a three-dimensional system are consistent with there being no de Almeida-Thouless line, although the new finite-size scaling approach does not rule one out. For the model corresponding to four space dimensions, the new and traditional finite-size scaling analyses give conflicting results, indicating the need for a better understanding of finite-size scaling of spin glasses in a magnetic field.