Mean field behaviour of spin systems with orthogonal interaction matrix

TL;DR

This paper investigates the mean field behavior of long-range spin systems with orthogonal interaction matrices, establishing generalized correlation factorization properties that extend classical results from simpler models.

Contribution

It introduces weighted factorization properties for correlation functions in complex spin systems with glassy behavior, generalizing known factorization rules.

Findings

Proves weighted correlation factorization in long-range spin models

Extends classical Curie-Weiss factorization to more complex systems

Provides mathematical framework for glassy spin systems

Abstract

For the long-range deterministic spin models with glassy behaviour of Marinari, Parisi and Ritort we prove weighted factorization properties of the correlation functions which represent the natural generalization of the factorization rules valid for the Curie-Weiss case.