Universality of chaos and ultrametricity in mixed p-spin models

TL;DR

This paper proves that chaos phenomena and ultrametricity in mixed p-spin models are universal across different environments, confirming physicists' long-standing belief about the universality of the Parisi solution in mean-field models.

Contribution

It establishes the disorder universality of chaos and ultrametricity in mixed p-spin models under mild assumptions, extending to other spin glass models and physical observables.

Findings

Universality of quenched disorder chaos in the Edwards-Anderson model

Quenched concentration of magnetization in EA and mixed p-spin models

Quenched self-averaging of the overlap in the random field Ising model

Abstract

We prove disorder universality of chaos phenomena and ultrametricity in the mixed p-spin model under mild moment assumptions on the environment. This establishes the long-standing belief among physicists that the Parisi solution in mean-field models is universal. Our results extend to universal properties of other physical observables in the mixed p-spin model as well as in different spin glass models. These include universality of quenched disorder chaos in the Edwards-Anderson (EA) model and quenched concentration for the magnetization in both EA and mixed p-spin models under non-Gaussian environments. In addition, we show quenched self-averaging for the overlap in the random field Ising model under small perturbation of the external field.