A Multi-Scale Spin-Glass Mean-Field Model

TL;DR

This paper introduces a multi-scale spin-glass model extending the Sherrington-Kirkpatrick framework, establishing a Parisi-type variational principle for its thermodynamic limit using advanced probabilistic techniques.

Contribution

It presents a novel multi-scale spin-glass model and proves a variational principle for its pressure, expanding the theoretical understanding of complex disordered systems.

Findings

Pressure per particle obeys a Parisi-type variational principle

Lower bounds obtained via Ruelle cascade and interpolation

Upper bounds derived from factorisation and synchronization techniques

Abstract

In this paper a multi-scale version of the Sherrington and Kirkpatrick model is introduced and studied. The pressure per particle in the thermodynamical limit is proved to obey a variational principle of Parisi type. The result is achieved by means of lower and upper bounds. The lower bound is obtained with a Ruelle cascade using the interpolation technique, while the upper bound exploits factorisation properties of the equilibrium measure and the synchronisation technique