1 2 Se p 20 01 Nonequilibrium critical dynamics of ferromagnetic spin systems

We use simple models (the Ising model in one and two dimensions, and the spherical model in arbitrary dimension) to put to the test some recent ideas on the slow dynamics of nonequilibrium systems. In this review the focus is on the temporal evolution of two-time quantities and on the violation of the fluctuation-dissipation theorem, with special emphasis given to nonequilibrium critical dynamics. Prologue The aim of this review is to summarise recent works devoted to the dynamics of ferromagnetic spin systems after a quench from infinite temperature to their critical temperature. The initial impetus for such an investigation was the desire to put to the test, on simple models, some recent ideas on the slow dynamics of nonequilibrium systems (aging of two-time quantities and violation of the fluctuation-dissipation theorem). By simple models we mean models with no quenched disorder, with, for some of them at least, the virtue of being solvable. Here we address the case of ferromagnetic spin systems, such as the Ising model in one and two dimensions, and the spherical model in arbitrary dimension. Urn models are also simple enough to serve the same purpose. They are the subject of another review in this volume [1]. During the course of this investigation we realised the interest of posing the same questions for nonequilibrium critical dynamics [2, 3]. 1. The fluctuation-dissipation theorem and its violation Consider a generic spin system evolving at constant temperature from a disordered initial configuration. Let s and t, with s < t, be two successive instants of time, and τ = t − s, their difference. Denoting by σ(t) the spin at time t, we consider the correlation C(t, s) = σ(s)σ(t),