The 1/m expansion in spin glasses and the de Almeida-Thouless line

TL;DR

This paper uses a 1/m expansion approach to analyze the lower critical dimension of the de Almeida-Thouless line in spin glasses, suggesting it is close to six, which aligns with numerical studies.

Contribution

It establishes a theoretical link between the lower critical dimension of the de Almeida-Thouless line and the large-m limit of m-vector spin glasses using a 1/m expansion.

Findings

Lower critical dimension of the de Almeida-Thouless line equals that of the large-m limit.

Numerical studies indicate this critical dimension is approximately six.

Abstract

It is shown by means of a 1/m expansion about the large-m limit of the m-vector spin glass that the lower critical dimension of the de Almeida-Thouless line in spin glasses is equal to the lower critical dimension of the large-m limit of the m-vector spin glass. Numerical studies suggest that this is close to six.