properties at a disordered critical point

We investigate, analytically near the dimension duc = 4 and numerically in d = 3, the non equilibrium relaxational dynamics of the randomly diluted Ising model at criticality. Using the Exact Renormalization Group Method to one loop, we compute the two times t, tw correlation function and Fluctuation Dissipation Ratio (FDR) for any Fourier mode of the order parameter, of finite wave vector q. In the large time separation limit, the FDR is found to reach a non trivial value X∞ independently of (small) q and coincide with the FDR associated to the the total magnetization obtained previously. Explicit calculations in real space show that the FDR associated to the local magnetization converges, in the asymptotic limit, to this same value X∞. Through a Monte Carlo simulation, we compute the autocorrelation function in three dimensions, for different values of the dilution fraction p at Tc(p). Taking properly into account the corrections to scaling, we find, according to the Renormalization Group predictions, that the autocorrelation exponent λc is independent on p. The analysis is complemented by a study of the non equilibrium critical dynamics following a quench from a completely ordered state.