Out of Equilibrium Solutions in the $XY$-Hamiltonian Mean Field model

TL;DR

This paper constructs out-of-equilibrium magnetized solutions for the $XY$-HMF model using uncoupled pendula and demonstrates an out-of-equilibrium phase transition with these solutions.

Contribution

It introduces a novel method to build out-of-equilibrium solutions in the $XY$-HMF model using integrable pendula, revealing a new phase transition.

Findings

Identification of out-of-equilibrium magnetized solutions

Demonstration of an out-of-equilibrium phase transition

Use of integrable pendula to model the solutions

Abstract

Out of equilibrium magnetised solutions of the $XY$-Hamiltonian Mean Field ($XY$-HMF) model are build using an ensemble of integrable uncoupled pendula. Using these solutions we display an out-of equilibrium phase transition using a specific reduced set of the magnetised solutions.