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,tw​)=[]av​ a typical
aging scenario with a t/tw​ scaling is established. Investigating spatial
correlations we find an algebraic growth law ξ(tw​)∼twα(T)​ of
the average domain size. The spatial correlation function G(r,tw​)=[<Si​(tw​)Si+r​(tw​)>2]av​ scales with r/ξ(tw​). 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 100×100)
and then we calculate the correlations between this state and the states
generated during a Monte Carlo simulation.Comment: 38 pages, RevTeX, 14 postscript figure