Competition between dynamic and thermal relaxation in non-equilibrium spin systems above the critical point

Abstract

We study the long-time behaviour and the spatial correlations of a simple ferromagnetic spin system whose kinetics is governed by a thermal bath with a time-dependent temperature which is characterized by a given external relaxation time tau. Exact results are obtained in the framework of the spherical model in d dimensions. In the paramagnetic phase, the long-time kinetics is shown to depend crucially on the ratio between tau and the internal equilibration time tau_eq. If tau is less than tau_eq, the model relaxes rapidly towards an equilibrium state but there appear transient and spatially oscillating contributions in the spin-spin correlation function. On the other hand, if tau is much greater than tau_eq the system is clamped and its time evolution is delayed with respect to the one of the heat bath. For waiting times s such that tau << s << tau_eq, a quasi-stationary state is found where the fluctuation-dissipation theorem does not hold.

Latex2e, 18 pp, 2 figures (final form)

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Cited by in corpus (5)

• Local scale-invariance and ageing in noisy systems
• Aging at Criticality in Model C Dynamics
• The kinetic spherical model in a magnetic field
• Critical percolation in the slow cooling of the bi-dimensional ferromagnetic Ising model
• Asymmetric Langevin dynamics for the ferromagnetic spherical model