Dynamic ultrametricity in finite dimensional spin glasses

We show results of simulations of a weakly driven four dimensional Edwards- Anderson spin glass, which presents clear signatures of dynamical ultrametricity at low temperatures. The presence of a hierarchical organization of time scales is evident from the appearance of a triangular relation between correlations at three characteristic long times in the asymptotic limit of small drive, and also in the scaling form of stationary correlations in this regime. The differences between this scenario and known results of the aging dynamics of the model are also analyzed.