A Monte Carlo Investigation of the Hamiltonian Mean Field Model

TL;DR

This paper uses Monte Carlo simulations to analyze the stability and thermodynamic properties of the Hamiltonian Mean Field model, confirming the instability of certain states below a critical energy density.

Contribution

It introduces a modified Monte Carlo method to test the stability of homogeneous Quasi Stationary States in the HMF model, providing numerical confirmation of their instability below a critical energy.

Findings

Homogeneous Quasi Stationary States are unstable below U~0.68.

Monte Carlo calculations match the caloric curve and finite size effects.

Results confirm Vlasov stability analysis predictions.

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.