Out of equilibrium phase transitions in mean field Hamiltonian dynamics

TL;DR

This paper reviews the Hamiltonian Mean Field model's out-of-equilibrium phase transitions, using Lynden-Bell's violent relaxation theory to predict transitions between homogeneous and inhomogeneous states, including phase diagram features.

Contribution

It applies Lynden-Bell's maximum entropy approach to analyze out-of-equilibrium phase transitions in the HMF model, revealing detailed phase diagrams with critical points.

Findings

Identification of first and second order phase transition lines

Presence of a tricritical point where transition lines merge

Conditions for stability of homogeneous phases

Abstract

Systems with long-range interactions display a short-time relaxation towards Quasi-Stationary States (QSSs), whose lifetime increases with system size. With reference to the Hamiltonian Mean Field (HMF) model, we here review Lynden-Bell's theory of ``violent relaxation''. The latter results in a maximum entropy scheme for a water-bag initial profile which predicts the presence of out-of-equilibrium phase transitions} separating homogeneous (zero magnetization) from inhomogeneous (non-zero magnetization) QSSs. Two different parametric representations of the initial condition are analyzed and the features of the phase diagram are discussed. In both representations we find a second order and a first order line of phase transitions that merge at a tricritical point. Particular attention is payed to the condition of existence and stability of the homogenous phase.