Nonequilibrium phase transitions and violent relaxation in the Hamiltonian mean-field model

We discuss the nature of nonequilibrium phase transitions in the Hamiltonian mean-field model using detailed numerical simulations of the Vlasov equation and molecular dynamics. Starting from fixed magnetization water bag initial distributions and varying the energy, the states obtained after a violent relaxation undergo a phase transition from magnetized to nonmagnetized states when going from lower to higher energies. The phase transitions are either first order or are composed of a cascade of phase reentrances. This result is at variance with most previous results in the literature mainly based on the Lynden-Bell theory of violent relaxation. The latter is a rough approximation and, consequently, is not suited for an accurate description of nonequilibrium phase transition in long-range interacting systems.