Ultrametricity in three-dimensional Edwards-Anderson spin glasses

We perform an accurate test of ultrametricity in the aging dynamics of the three-dimensional Edwards-Anderson spin glass. Our method consists in consi dering the evolution in parallel of two identical systems constrained to ha ve fixed overlap. This turns out to be a particularly efficient way to stud y 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 u s to infer that dynamical ultrametricity implies the same property at the l evel of equilibrium states.