Glassy phase in the Hamiltonian Mean Field model

We study the relaxation dynamics of a Hamiltonian system of N fully coupled XY spins. The thermodynamics of the system predicts a ferromagnetic and a paramagnetic phase. Starting from out-of-equilibrium initial conditions, the dynamics at constant energy drives the system into quasistationary states (QSSs) characterized by dynamical frustration. We introduce the spin polarization as an order parameter which allows us to interpret the dynamically generated QSS regime as a glassy phase of the model.