The Mpemba effect in spin glasses: a persistent memory effect.

When a hot system cools faster than an initially colder one, and both are refrigerated in the same thermal reservoir, we have the so called Mpemba effect. Its features have bee discussed in many contexts, and, even if in many cases even its existence is far from easy to shows, it is clear that in different contexts it can have very different roots.

We discuss here the fact that the Mpemba effect exists in spin glasses, and that it is a non-equilibrium process, governed by the coherence length of the system. The effect occurs when the bath temperature is below the transition temperature to the glassy phase, even under thermal protocols that do not cross the critical temperature, and it follows from a strong relationship between the internal energy and the correlation length. It can be seen as an interesting direction towards the experimental study of the coherence length in super-cooled liquids and other glass formers.