The dynamics of the spherical p-spin model: from microscopic to asymptotics

We have numerically investigated the mean-field dynamics of the the $p$-spin interaction spin glass model with p=3 using an efficient method of integrating the dynamic equations. We find a new time scale associated with the onset of the breakdown of the fluctuation-dissipation theorem in the intermediate time regime. We also find that the off-equilibrium relaxation exhibits a sub-aging behavior in the intermediate times and crosses over to a simple aging in the asymptotic regime.