Spin glass models with Kac interactions

TL;DR

This paper reviews spin glass models with Kac interactions, exploring their relation to mean field theory and efforts to extend beyond it, focusing on systems with finite interaction ranges.

Contribution

It introduces and analyzes spin glass models with Kac interactions, connecting finite-range systems to mean field theory and discussing approaches to go beyond mean field approximations.

Findings

Relation between Kac spin glass models and mean field theory established

Insights into finite interaction range effects on spin glasses

Initial attempts to extend beyond mean field theory discussed

Abstract

In this paper I will review my work on disordered systems -spin glass model with two body and $p>2$ body interactions- with long but finite interaction range $R$. I will describe the relation of these model with Mean Field Theory in the Kac limit and some attempts to go beyond mean field.