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

C. Godreche, J. M. Luck

Published 2000-01-19Version 1

We study the dynamics of ferromagnetic spin systems quenched from infinite temperature to their critical point. We show that these systems are aging in the long-time regime, i.e., their two-time autocorrelation and response functions and associated fluctuation-dissipation ratio are non-trivial scaling functions of both time variables. This is exemplified by the exact analysis of the spherical model in any dimension D>2, and by numerical simulations on the two-dimensional Ising model. We show in particular that, for $1\ll s$ (waiting time) $\ll t$ (observation time), the fluctuation-dissipation ratio possesses a non-trivial limit value $X_\infty$, which appears as a dimensionless amplitude ratio, and is therefore a novel universal characteristic of non-equilibrium critical dynamics. For the spherical model, we obtain $X_\infty=1-2/D$ for 2<D<4, and $X_\infty=1/2$ for D>4 (mean-field regime). For the two-dimensional Ising model we measure $X_\infty\approx0.26\pm0.01$.