Time and length scales in spin glasses

We discuss the slow, nonequilibrium, dynamics of spin glasses in their glassy phase. We briefly review the present theoretical understanding of the spectacular phenomena observed in experiments and describe new numerical results obtained in the first large-scale simulation of the nonequilibrium dynamics of the three-dimensional Heisenberg spin glass. 1. Why do we study spin glass dynamics? Spin glasses can be seen as one of the paradigms for the statistical mechanics of impure materials. Experimentally, however, the spin glass phase is always probed via nonequilibrium dynamic experiments, because the equilibration time of macroscopic samples is infinite. Simulations can probe equilibrium behaviour for very moderate sizes only, so the thermodynamic nature of the spin glass phase is still a matter of debate. It is also as a model system that the glassy dynamics of spin glasses has been studied very extensively in experiments, simulations, and theoretically in the last two decades [1, 2]. Although many theories account for the simplest experimental results, such as the ageing phenomenon, earl