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

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.

4 pages (plus a few lines), 3 figures. v2: minor error corrected. v3: numerics supplemented by analytical arguments, references added, figure of density of states added