Effects of superaging and percolation crossover on the nonequilibrium critical behavior of the two-dimensional disordered Ising model

A Monte Carlo study of the specific features of the nonequilibrium critical behavior has been performed for the two-dimensional “pure” and structurally disordered Ising models in the course of their evolution from the low-temperature initial state at spin concentrations $p= 1.0$, $0.9$, and $0.8$. It is shown for the first time that the pinning of domain walls by structural defects leads to the anomalously strong slowing down in the evolution of the autocorrelation function characterized by the superaging effect with exponents $\mu=6.25(5)$ and $\mu=6.75(5)$ for the model with the spin concentrations $p=0.9$ and $0.8$, respectively. The pure model exhibits the conventional aging with the exponent $\mu=1$. It is found that the superaging effects in structurally disordered systems lead to vanishing of the limiting fluctuation-dissipation ratio $X^{\infty}$, whereas $X^{\infty}= 0.751(24)$ for the pure model.