Abstract
We show results of simulations of a weakly driven four-dimensional Edwards-Anderson (EA) spin glass, which present 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 characterisitc long times in the asymptotic limit of small drive, and also in the scaling form of stationary correlations in this regime. Recent results in the three-dimensional case have been inconclusive showing the importance of dimensionality in tackling this delicate problem.