Distribution of time scales in the Sherrington-Kirkpatrick model

Abstract

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 $N^{1/3} (T_c-T)$ strengthening the belief that $\overline{\ln\tau}\propto N^{1/3}$ in the whole spin glass phase.