Central limit theorem for the overlaps on the Nishimori line

TL;DR

This paper proves that the joint distribution of rescaled overlaps in the Nishimori line of the Sherrington-Kirkpatrick model converges to a Gaussian vector, extending understanding of overlap behavior in spin glasses.

Contribution

It establishes a central limit theorem for the joint distribution of overlaps on the Nishimori line, a significant advancement in spin glass theory.

Findings

Joint distribution of overlaps converges to Gaussian

Overlap distribution is self-averaging for large volumes

Provides a CLT for rescaled overlaps

Abstract

The overlap distribution of the Sherrington-Kirkpatrick model on the Nishimori line has been proved to be self averaging for large volumes. Here we study the joint distribution of the rescaled overlaps around their common mean and prove that it converges to a Gaussian vector.