Glassy phase in the Hamiltonian Mean Field model

TL;DR

This paper investigates the relaxation dynamics of a fully-coupled XY spin system, revealing a glassy phase characterized by dynamical frustration and introducing a new order parameter, spin polarization, to interpret quasi-stationary states.

Contribution

It introduces spin polarization as a novel order parameter to identify a glassy phase in the Hamiltonian Mean Field model, linking dynamical frustration to glassy behavior.

Findings

Identification of a glassy phase via spin polarization

Quasi-stationary states exhibit dynamical frustration

System relaxes into non-equilibrium states with glassy characteristics

Abstract

We study the relaxation dynamics of a Hamiltonian system of N fully-coupled XY spins. The thermodynamics of the system predicts a ferromagnetic and a paramagnetic phase. Starting from out-of-equilibrium initial conditions, the dynamics at constant energy drives the system into quasi-stationary states (QSS) characterized by dynamical frustration. We introduce the spin polarization as a new order parameter which allows to interpret the dynamically generated QSS regime as a glassy phase of the model.