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

TL;DR

This paper investigates how the interplay between thermal and dynamic relaxation times influences the long-term behavior and spatial correlations in a non-equilibrium ferromagnetic spin system, revealing different relaxation regimes.

Contribution

It provides exact analytical results for the spherical model showing how the ratio of external to internal relaxation times affects relaxation dynamics and correlations.

Findings

Rapid relaxation with transient oscillations when tau < tau_eq

Delayed evolution and violation of fluctuation-dissipation theorem when tau >> tau_eq

Identification of a quasi-stationary state in intermediate times

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.