Ageing and non-equilibrium critical phenomena in Monte Carlo simulations

Abstract

It is considered the non-equilibrium critical evolution of statistical systems which displays some features, such as ageing and violation of the fluctuation-dissipation theorem. We review here some theoretical results of computations that have been obtained in recent years for universal quantities, such as the exponents determining the scaling behaviour of dynamic response and correlation functions and the fluctuation-dissipation ratio, associated with the non-equilibrium critical dynamics, with particular focus on the 3D pure and diluted Ising models with Glauber dynamics. We analyse an influence of critical fluctuations, different non-equilibrium initial states and presence of nonmagnetic impurities in spin systems on two-time dependence of correlation and response functions on characteristic time variables as waiting time tw and time of observation t – tw with t > tw. We discuss the obtained values of non-equilibrium exponents for autocorrelation and response functions and values of the universal long-time limit of the fluctuation-dissipation ratio X∞. Analysis of simulation results show that the insertion of disorder leads to new values of X∞ with X∞diluted > X∞pure.