Aging and non-equilibrium critical phenomena in Monte Carlo simulations of 3D pure and diluted Ising models

We investigate the non-equilibrium critical evolution of statistical systems and describe of its some features, such as aging and violation of the fluctuation-dissipation theorem. We consider some theoretical results of computations for universal quantities that have been obtained in recent years, such as the exponents determining the scaling behavior of dynamic response and correlation functions and the fluctuation-dissipation ratio, associated with the non-equilibrium critical dynamics. We derive our original Monte Carlo simulation results for 3D pure and diluted Ising models with Glauber and Metropolis dynamics. For these models, we analyze the influence of critical fluctuations, different non-equilibrium initial states, and the presence of nonmagnetic impurities on the two-time dependence of correlation and response functions on characteristic time variables, such as waiting time $t_{\rm w}$ and time of observation $t - t_{\rm w}$ with $t>t_{\rm w}$ . We discuss the obtained values of the non-equilibrium exponents for the autocorrelation and response functions and values of the universal long-time limit of the fluctuation-dissipation ratio $X^{\infty }$ . Our simulation results demonstrate that the insertion of disorder leads to new values of $X^{\infty }$ with $X_{\rm diluted}^{\infty }>X_{\rm pure}^{\infty }$ .