Ultrametricity in 3D Edwards-Anderson spin glasses

TL;DR

This paper provides evidence for dynamical ultrametricity in the aging behavior of 3D Edwards-Anderson spin glasses, distinguishing it from simpler aging systems and linking dynamics to equilibrium properties.

Contribution

It introduces an efficient method to test ultrametricity in spin glasses and demonstrates its presence in their aging dynamics, connecting it to equilibrium states.

Findings

Strong evidence for dynamical ultrametricity in spin glasses

Ultrametricity absent in simpler aging systems

Links between aging dynamics and equilibrium ultrametricity

Abstract

We perform an accurate test of Ultrametricity in the aging dynamics of the three dimensional Edwards-Anderson spin glass. Our method consists in considering the evolution in parallel of two identical systems constrained to have fixed overlap. This turns out to be a particularly efficient way to study the geometrical relations between configurations at distant large times. Our findings strongly hint towards dynamical ultrametricity in spin glasses, while this is absent in simpler aging systems with domain growth dynamics. A recently developed theory of linear response in glassy systems allows to infer that dynamical ultrametricity implies the same property at the level of equilibrium states.