Ultrametricity in 3D Edwards-Anderson spin glasses

摘要

We perform an accurate test of Ultrametricity in the aging dynamics of thethree dimensional Edwards-Anderson spin glass. Our method consists inconsidering the evolution in parallel of two identical systems constrained tohave fixed overlap. This turns out to be a particularly efficient way to studythe geometrical relations between configurations at distant large times. Ourfindings strongly hint towards dynamical ultrametricity in spin glasses, whilethis is absent in simpler aging systems with domain growth dynamics. A recentlydeveloped theory of linear response in glassy systems allows to infer thatdynamical ultrametricity implies the same property at the level of equilibriumstates.