Distribution of time scales in the Sherrington-Kirkpatrick model

Numerical data on the probability distribution of the equilibrium relaxation time of the Sherrington-Kirkpatrick model are obtained by means of dynamical Monte Carlo simulation, for several values of the system size $N$ and temperature $T$. Proper care is taken that the thermal fluctuations on the relaxation time estimates are totally negligible compared to the disorder induced fluctuations. The probability distribution of $\ln \tau -\overline{\ln \tau }$ scales with the scaling variable $N^{1\mathrm{/}3}(T_c-T)$ strengthening the belief that $\overline{\ln \tau }\propto N^{1\mathrm{/}3}$ in the whole spin glass phase.