  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 phase transition. 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 respectively initial magnetization equal to one (M1 IC) and
equal to zero (M0 IC). We compare the corresponding $\mu$-space, the resulting
velocity pdfs and correlations, and the eventual aging features of the
microscopic dynamics. In both cases the model exhibits non-gaussian pdfs,
though anomalous correlations are present only when the system is started with
an initial magnetization 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
reproduced by a Tsallis q-exponential function. These results contribute to
clarify the overall scenario, which is more complex than previously expected
and stress the importance of the dynamics in the relaxation process. The
nonextensive statistical mechanics formalism proposed by Tsallis seems to be
valid, in the out-of-equilibrium phase, when correlations and strong long-term
memory effects emerge. This regime becomes stable if the $N\to \infty $ limit
is performed before the $t\to \infty $ limit.
