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 $d=1\mathrm{}$ and $2$. We find $r_{d=1\mathrm{}}=0.45\mathrm{}\pm 0.05$ and $r_{d=2\mathrm{}}=0.23\mathrm{}\pm 0.05$ for the Bak-Sneppen model, and our results suggest $r=1/4\mathrm{}$ for the analytically tractable multitrade model in both dimensions.