Factorization properties in d-dimensional spin glasses. Rigorous results and some perspectives

TL;DR

This paper proves that d-dimensional Gaussian spin glass models exhibit stochastic stability, satisfy Ghirlanda-Guerra identities, and possess ultrametricity, providing rigorous insights into their structural properties.

Contribution

It establishes rigorous proofs of stability, Ghirlanda-Guerra identities, and ultrametricity in d-dimensional Gaussian spin glasses, advancing theoretical understanding.

Findings

Models are strongly stochastically stable

Models fulfill Ghirlanda-Guerra identities in distribution

Models exhibit ultrametricity

Abstract

In this paper we show that d-dimensional Gaussian spin glass models are strongly stochastically stable, fulfill the Ghirlanda-Guerra identities in distribution and the ultrametricity property.