Phase transitions of quasistationary states in the Hamiltonian Mean Field model

TL;DR

This paper investigates the out-of-equilibrium phase transitions in the Hamiltonian Mean Field model under an external magnetic field, confirming Lynden-Bell's theory through numerical simulations and exploring the effects of the field on phase behavior.

Contribution

It demonstrates the applicability of Lynden-Bell's theory to out-of-equilibrium dynamics with an external field and characterizes the phase transition and susceptibility phenomena in the HMF model.

Findings

Existence of out-of-equilibrium phase transition between magnetized and non-magnetized states.

External magnetic field removes the phase transition at equilibrium.

Negative susceptibility regions are observed, aligning with theoretical predictions.

Abstract

The out-of-equilibrium dynamics of the Hamiltonian Mean Field (HMF) model is studied in presence of an externally imposed magnetic field h. Lynden-Bell's theory of violent relaxation is revisited and shown to adequately capture the system dynamics, as revealed by direct Vlasov based numerical simulations in the limit of vanishing field. This includes the existence of an out-of-equilibrium phase transition separating magnetized and non magnetized phases. We also monitor the fluctuations in time of the magnetization, which allows us to elaborate on the choice of the correct order parameter when challenging the performance of Lynden-Bell's theory. The presence of the field h removes the phase transition, as it happens at equilibrium. Moreover, regions with negative susceptibility are numerically found to occur, in agreement with the predictions of the theory.