  The low temperature dynamics of the two- and three-dimensional Ising spin
glass model with Gaussian couplings is investigated via extensive Monte Carlo
simulations. We find an algebraic decay of the remanent magnetization. For the
autocorrelation function $C(t,t_w)=[< S_i(t+t_w)S_i(t_w)>]_{av}$ a typical
aging scenario with a $t/t_w$ scaling is established. Investigating spatial
correlations we find an algebraic growth law $\xi(t_w)\sim t_w^{\alpha(T)}$ of
the average domain size. The spatial correlation function $G(r,t_w)=[<
S_i(t_w)S_{i+r}(t_w)>^2]_{av}$ scales with $r/\xi(t_w)$. The sensitivity of the
correlations in the spin glass phase with respect to temperature changes is
examined by calculating a time dependent overlap length. In the two dimensional
model we examine domain growth with a new method: First we determine the exact
ground states of the various samples (of system sizes up to $100\times 100$)
and then we calculate the correlations between this state and the states
generated during a Monte Carlo simulation.
