Generalised Bose-Einstein phase transition in large-$m$ component spin glasses

TL;DR

This paper explores a novel phase transition in large-$m$ component spin glasses, proposing a $1/m$ expansion approach that predicts a replica symmetric state and reveals a Bose-Einstein-like transition with unique characteristics.

Contribution

It introduces a $1/m$ expansion method for finite-dimensional spin glasses and uncovers a Bose-Einstein-like phase transition in the infinite-$m$ limit.

Findings

Predicts a replica symmetric state in finite dimensions

Identifies a Bose-Einstein-like phase transition with $N^{2/5}$ macroscopically occupied states

Provides a new theoretical framework for understanding spin glass phases

Abstract

It is proposed to understand finite dimensional spin glasses using a $1/m$ expansion, where $m$ is the number of spin components. It is shown that this approach predicts a replica symmetric state in finite dimensions. The point about which the expansion is made, the infinite-$m$ limit, has been studied in the mean-field limit in detail and has a very unusual phase transition, rather similar to a Bose-Einstein phase transition but with $N^{2/5}$ macroscopically occupied low-lying states.