  We present a Monte Carlo numerical investigation of the Hamiltonian Mean
Field (HMF) model. We begin by discussing canonical Metropolis Monte Carlo
calculations, in order to check the caloric curve of the HMF model and study
finite size effects. In the second part of the paper, we present numerical
simulations obtained by means of a modified Monte Carlo procedure with the aim
to test the stability of those states at minimum temperature and zero
magnetization (homogeneous Quasi Stationary States) which exist in the
condensed phase of the model just below the critical point. For energy
densities smaller than the limiting value $U\sim 0.68$, we find that these
states are unstable, confirming a recent result on the Vlasov stability
analysis applied to the HMF model.
