Dynamics and nonequilibrium states in the Hamiltonian mean-field model: A closer look

TL;DR

This paper critically examines the existence of quasistationary states in the Hamiltonian mean-field model, revealing slow relaxation but no evidence of quasistationarity during early evolution, and highlighting nonergodic behavior.

Contribution

It provides a detailed analysis showing the absence of quasistationary states in early dynamics and discusses nonergodic properties affecting statistical descriptions.

Findings

No evidence of quasistationary states during early evolution

Slow relaxation observed at long times

Nonergodic properties influence energy distribution in final states

Abstract

We critically revisit the evidence for the existence of quasistationary states in the globally coupled XY (or Hamiltonian mean-field) model. A slow-relaxation regime at long times is clearly revealed by numerical realizations of the model, but no traces of quasistationarity are found during the earlier stages of the evolution. We point out the nonergodic properties of this system in the short-time range, which makes a standard statistical description unsuitable. New aspects of the evolution during the nonergodic regime, and of the energy distribution function in the final approach to equilibrium, are disclosed.