Aging exponents in self-organized criticality

In a recent Letter [Phys. Rev. Lett. 79, 889 (1997)] we demonstrated that the avalanches in the Bak-Sneppen model display aging behavior similar to glassy systems. Numerical results for temporal correlations show a broad distribution with two distinct regimes separated by a time scale that is related to the age of the avalanche. This dynamical breaking of time-translational invariance results in a previously unrecognized critical exponent r. Here we present results for r from extensive numerical simulations of self-organized critical models in d=1 and 2. We find r_d=1=0.45±0.05 and r_d=2=0.23±0.05 for the Bak-Sneppen model, and our results suggest r=1/4 for the analytically tractable multitrade model in both dimensions.