Nonequilibrium critical dynamics of the two-dimensionalXYmodel

The nonequilibrium critical dynamics of the two-dimensional XY model is investigated numerically through Monte Carlo simulations and analytically in the spin-wave approximation. We focus in particular on the behaviour of the two-time response and correlation functions and show that the ageing dynamics depends on the initial conditions. The presence of critical fluctuations leads to nontrivial violations of the fluctuation-dissipation theorem apparently reminiscent of the three-dimensional Edwards-Anderson spin glass model. We compute for this reason the finite-size overlap probability distribution function and find that it is related to the finite-time fluctuation-dissipation ratio obtained in the out-of-equilibrium dynamics, provided that the temperature is not very low.