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

C. Godrèche (1) , J.M. Luck (2)

1 SPEC - UMR3680 - Service de physique de l'état condensé
2 SPhT - Service de Physique Théorique

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 $24$ (mean-field regime). For the two-dimensional Ising model we measure $X_\infty\approx0.26\pm0.01.$

Domaines: Physique Générale [physics.gen-ph]; Autre [cond-mat.other]

C. Godrèche, J.M. Luck. Response of non-equilibrium systems at criticality: ferromagnetic models in dimension two and above. Journal of Physics A: Mathematical and Theoretical, 2000, 33, pp.9141-9164. ⟨10.1088/0305-4470/33/50/302⟩. ⟨hal-00103069⟩