  We study the non-equilibrium time evolution of the classical XY spin model in
two dimensions. The two-time autocorrelation and linear response functions are
considered for systems initially prepared in a high temperature state and in a
completely ordered state. After a quench into the critical phase, we determine,
via Monte Carlo simulations, the time-evolution of these quantities and extract
the temperature dependence of the slope of the parametric plot
susceptibility/correlation in the asymptotic regime. This slope is usually
identified with the infinite fluctuation-dissipation ratio which measures the
violation to the equilibrium fluctuation-dissipation theorem. However, a direct
measure of this ratio leads to a vanishing value.
