Metastability and anomalous behavior in the HMF model: connections to nonextensive thermodynamics and glassy dynamics

We review some of the most recent results on the dynamics of the Hamiltonian Mean Field (HMF) model, a systems of N planar spins with ferromagnetic infinite-range interactions. We show, in particular, how some of the dynamical anomalies of the model can be interpreted and characterized in terms of the weak-ergodicity breaking proposed in the framework of glassy systems. We also discuss the connections with the nonextensive thermodynamics proposed by Tsallis.