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We study the dynamics of ferromagnetic spin systems quenched from infinitetemperature to their critical point. We show that these systems are aging inthe long-time regime, i.e., their two-time autocorrelation and responsefunctions and associated fluctuation-dissipation ratio are non-trivial scalingfunctions of both time variables. This is exemplified by the exact analysis ofthe spherical model in any dimension D>2, and by numerical simulations on thetwo-dimensional Ising model. We show in particular that, for $1\ll s$ (waitingtime) $\ll t$ (observation time), the fluctuation-dissipation ratio possesses anon-trivial limit value $X_\infty$, which appears as a dimensionless amplituderatio, and is therefore a novel universal characteristic of non-equilibriumcritical dynamics. For the spherical model, we obtain $X_\infty=1-2/D$ for2<D<4, and $X_\infty=1/2$ for D>4 (mean-field regime). For the two-dimensionalIsing model we measure $X_\infty\approx0.26\pm0.01$.Comment: 31 pages, 5 figure

Response of non-equilibrium systems at criticality: ferromagnetic models in dimension two and above