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

Source: [Competition between dynamic and thermal relaxation in non-equilibrium spin systems above the critical point](<https://www.sota2.com/research/paper/68fa22947a2b558e2933c856>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T05:01:57.088Z

Authors: Alan Picone, Malte Henkel, Jean Richert

Published: 2002-10-15T16:51:50.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/0210330>)

[PDF](<https://arxiv.org/pdf/cond-mat/0210330.pdf>)