Dynamics and thermodynamics of a simple model similar to self-gravitating systems: the HMF model

TL;DR

The paper explores the Hamiltonian Mean Field (HMF) model as a simplified system that captures key features of self-gravitating systems, providing insights into their dynamics, thermodynamics, and phase transitions.

Contribution

It establishes a detailed analogy between the HMF model and self-gravitating systems, applying plasma physics techniques to analyze their behavior and implications.

Findings

HMF model exhibits features like phase transitions and metastable states.

The analogy helps understand the impact of interaction potential form.

Applications to astrophysics, such as galaxy bar formation.

Abstract

We discuss the dynamics and thermodynamics of the Hamiltonian Mean Field model (HMF) which is a prototypical system with long-range interactions. The HMF model can be seen as the one Fourier component of a one-dimensional self-gravitating system. Interestingly, it exhibits many features of real self-gravitating systems (violent relaxation, persistence of metaequilibrium states, slow collisional dynamics, phase transitions,...) while avoiding complicated problems posed by the singularity of the gravitational potential at short distances and by the absence of a large-scale confinement. We stress the deep analogy between the HMF model and self-gravitating systems by developing a complete parallel between these two systems. This allows us to apply many technics introduced in plasma physics and astrophysics to a new problem and to see how the results depend on the dimension of space and on the form of the potential of interaction. This comparative study brings new light in the statistical mechanics of self-gravitating systems. We also mention simple astrophysical applications of the HMF model in relation with the formation of bars in spiral galaxies.