  We present a high statistic systematic study of the overlap correlation
function well below the critical temperature in the three dimensional Gaussian
spin glass. The off-equilibrium correlation function has been studied
confirming the power law behavior for the dynamical correlation length. In
particular we have computed the dynamical critical exponent $z$ in a wide range
of temperatures, $0.35 \le T \le 0.9$, obtaining a dependence $z(T)=6.2/T$ in a
very good agreement with recent experiments. Moreover, we report a study of the
violation of the fluctuation-dissipation theorem for very low temperatures
$T=0.5$ and $T=0.35$. All our numerical results avoid a droplet model
interpretation even when $T$ is as low as $T=0.35$.

Disordered Systems and Neural Networks;Statistical Mechanics