Core-halo distribution in the Hamiltonian Mean-Field Model

TL;DR

This paper investigates the Hamiltonian Mean-Field Model, revealing a core-halo structure in its stationary state, non-ergodic behavior, and a non-equilibrium phase transition, with predictive dynamical methods for distributions.

Contribution

It demonstrates that the HMF model's stationary state has a unique core-halo structure and can be predicted using dynamical properties without adjustable parameters.

Findings

Stationary state exhibits core-halo distribution

HMF is non-ergodic and non-mixing in the thermodynamic limit

Identifies a non-equilibrium first-order phase transition

Abstract

We study a paradigmatic system with long-range interactions: the Hamiltonian Mean-Field Model (HMF). It is shown that in the thermodynamic limit this model does not relax to the usual equilibrium Maxwell-Boltzmann distribution. Instead, the final stationary state has a peculiar core-halo structure. In the thermodynamic limit, HMF is neither ergodic nor mixing. Nevertheless, we find that using dynamical properties of Hamiltonian systems, it is possible to quantitatively predict both the spin distribution and the velocity distribution functions in the final stationary state, without any adjustable parameters. We also show that HMF undergoes a non-equilibrium first-order phase transition between paramagnetic and ferromagnetic states.