Nonequilibrium phase transitions in systems with long-range interactions

TL;DR

This paper introduces a generalized Hamiltonian Mean Field model with multiple phases, revealing discrepancies between statistical mechanics predictions and dynamical simulations, highlighting the importance of dynamics in long-range interacting systems.

Contribution

The paper presents a new gHMF-XY model with explicit Hamiltonian dynamics and a dynamical theory that accurately predicts phase diagrams without adjustable parameters.

Findings

Microcanonical phase diagram differs from molecular dynamics results.

Dynamics are crucial for understanding long-range systems.

BG statistics are inadequate for these systems.

Abstract

We introduce a generalized Hamiltonian Mean Field Model (gHMF)-XY model with both linear and quadratic coupling between spins and explicit Hamiltonian dynamics. In addition to the usual paramagnetic and ferromagnetic phases, this model also possesses a nematic phase. The gHMF can be solved explicitly using Boltzmann-Gibbs (BG) statistical mechanics, in both canonical and microcanonical ensembles. However, when the resulting microcanonical phase diagram is compared with the one obtained using molecular dynamics simulations, it is found that the two are very different. We will present a dynamical theory which allows us to explicitly calculate the phase diagram obtained using molecular dynamics simulations without any adjustable parameters. The model illustrates the fundamental role played by dynamics as well the inadequacy of BG statistics for systems with long-range forces in the thermodynamic limit.