We investigate, analytically near the dimension $d_{uc}=4$ and numerically in $d=3$, the nonequilibrium relaxational dynamics of the randomly diluted Ising model at criticality. Using the exact renormalization-group method to one loop, we compute the two times $t,t_w$ 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 nontrivial value $X^{\infty }$ independently of (small) $q$ and coincide with the FDR associated to 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 $X^{\infty }$. Through a Monte Carlo simulation, we compute the autocorrelation function in three dimensions, for different values of the dilution fraction $p$ at $T_c\left(p\right)$. Taking properly into account the corrections to scaling, we find, according to the renormalization-group predictions, that the autocorrelation exponent ${\lambda }_c$ is independent of $p$. The analysis is complemented by a study of the nonequilibrium critical dynamics following a quench from a completely ordered state.

• Received 11 January 2005

DOI:https://doi.org/10.1103/PhysRevE.72.016105