Long time behavior of quasi-stationary states of the Hamiltonian Mean-Field model

TL;DR

This paper investigates the long-time behavior of quasi-stationary states in the Hamiltonian Mean-Field model, introducing a new numerical method to analyze their lifetime and showing their persistence across phase transition temperatures.

Contribution

A novel numerical tool based on phase fluctuations of magnetization is introduced to study and quantify the lifetime of quasi-stationary states in the Hamiltonian Mean-Field model.

Findings

Quasi-stationary states exist both below and above the critical temperature.

The lifetime of these states is significantly longer at supercritical temperatures.

The new observable effectively measures the lifetime of out-of-equilibrium states.

Abstract

The Hamiltonian Mean-Field model has been investigated, since its introduction about a decade ago, to study the equilibrium and dynamical properties of long-range interacting systems. Here we study the long-time behavior of long-lived, out-of-equilibrium, quasi-stationary dynamical states, whose lifetime diverges in the thermodynamic limit. The nature of these states has been the object of a lively debate, in the recent past. We introduce a new numerical tool, based on the fluctuations of the phase of the instantaneous magnetization of the system. Using this tool, we study the quasi-stationary states that arise when the system is started from different classes of initial conditions, showing that the new observable can be exploited to compute the lifetime of these states. We also show that quasi-stationary states are present not only below, but also above the critical temperature of the second order magnetic phase transition of the model. We find that at supercritical temperatures the lifetime is much larger than at subcritical temperatures.