Out-of-equilibrium tricritical point in a system with long-range interactions

TL;DR

This paper investigates out-of-equilibrium phase transitions in a long-range interacting system, revealing a tricritical point and metastability phenomena through theoretical predictions and numerical validation.

Contribution

It introduces a maximum entropy framework based on Lynden-Bell's violent relaxation to predict out-of-equilibrium phase transitions in the Hamiltonian Mean Field model.

Findings

Identification of first and second order phase transition lines.

Prediction and numerical confirmation of a tricritical point.

Observation of metastability near the first-order transition.

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 show that a maximum entropy principle, based on Lynden-Bell's pioneering idea of "violent relaxation", predicts the presence of out-of-equilibrium phase transitions separating the relaxation towards homogeneous (zero magnetization) or inhomogeneous (non zero magnetization) QSSs. When varying the initial condition within a family of "water-bags" with different initial magnetization and energy, first and second order phase transition lines are found that merge at an out--of--equilibrium tricritical point. Metastability is theoretically predicted and numerically checked around the first-order phase transition line.