The infinite volume limit in generalized mean field disordered models

TL;DR

This paper extends a proof strategy for the thermodynamic limit to a broader class of mean field spin glass models, including multi-component spins, combined interactions, and coupled replicas.

Contribution

It introduces a generalized approach to establish the existence of the thermodynamic limit across diverse mean field spin glass systems.

Findings

Proves the thermodynamic limit for models with multi-component spins.

Extends the method to systems with combined Curie-Weiss and spin glass interactions.

Handles coupled replica systems with overlap-dependent interactions.

Abstract

We generalize the strategy, we recently introduced to prove the existence of the thermodynamic limit for the Sherrington-Kirkpatrick and p-spin models, to a wider class of mean field spin glass systems, including models with multi-component and non-Ising type spins, mean field spin glasses with an additional Curie-Weiss interaction, and systems consisting of several replicas of the spin glass model, where replicas are coupled with terms depending on the mutual overlaps.