A Monte Carlo Investigation of the Hamiltonian Mean Field Model

Abstract

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.