Metastable states, anomalous distributions and correlations in the HMF model

We study the microscopic dynamics of the metastable quasi-stationary states (QSS) in the Hamiltonian mean field (HMF)model, a Hamiltonian system of N classical inertial spins with infinite-range interactions which shows a second-order phasetransition. In order to understand the origin of metastability, which appears in an energy region below the critical point,we consider two different classes of out-of-equilibrium initial conditions, both leading to QSS, and having respectivelyinitial magnetization equal to one (M1 IC) and equal to zero (M0 IC). We compare the corresponding μ-space, the resultingvelocity pdfs and correlations, and the eventual aging features of the microscopic dynamics. In both cases themodel exhibits nongaussian pdfs, though anomalous correlations are present only when the system is started with an initialmagnetization equal to one. In the M0 IC case the relaxation to equilibrium is almost exponential, while, for M1 IC,when correlations and aging are found, the decay is a power law and the overall behavior can be very well reproducedby a Tsallis q-exponential function. These results contribute to clarify the overall scenario, which is more complex thanpreviously expected and stress the importance of the dynamics in the relaxation process. The nonextensive statistical mechanicsformalism proposed by Tsallis seems to be valid, in the out-of-equilibrium phase, when correlations and stronglong-term memory effects emerge. This regime becomes stable if the N → ∞limit is performed before the t → ∞ limit.