  Following quenches of initial configurations having long range spatial
correlations, prepared at the demixing critical point, to points inside the
miscibility gap, we study aging phenomena in solid binary mixtures. Results on
the decay of the two-time order-parameter autocorrelation functions, obtained
from Monte Carlo simulations of the two-dimensional Ising model, with Kawasaki
exchange kinetics, are analyzed via state-of-the art methods. The outcome is
compared with that obtained for the ordering in uniaxial ferromagnets. For the
latter, we have performed Monte Carlo simulations of the same model using the
Glauber mechanism. For both types of systems we provide comparative discussion
of our results with reference to those concerning quenches with configurations
having no spatial correlation. We also discuss the role of structure on the
decay of these correlations.
