Nonequilibrium phase transitions and violent relaxation in the Hamiltonian Mean Field model

TL;DR

This paper investigates nonequilibrium phase transitions in the Hamiltonian Mean Field model through numerical simulations, revealing complex transition behaviors that challenge previous theoretical approximations like Lynden-Bell theory.

Contribution

It provides a detailed numerical analysis of phase transitions in the HMF model, showing the limitations of Lynden-Bell theory for describing violent relaxation.

Findings

Phase transitions from magnetized to non-magnetized states with increasing energy.

Existence of first order and cascade of reentrant phase transitions.

Lynden-Bell theory is inadequate for accurate description of these transitions.

Abstract

We discuss the nature of nonequilibrium phase transitions in the Hamiltonian Mean Field model using detailed numerical simulation of the Vlasov equation and molecular dynamics. Starting from fixed magnetization waterbag initial distributions and varying the energy, the states obtained after a violent relaxation undergoes a phase transition from magnetized to non-magnetized states when going from lower to higher energies. The phase transitions are either first order or composed by a cascade of phase reentrances. This result is at variance with most previous results in the literature mainly based in Lynden-Bell theory of violent relaxation. The latter is a rough approximation and consequently not suited for an accurate description of nonequilibrium phase transition in long range interacting systems.