Phase diagram of self-attracting systems

TL;DR

This paper explores the phase behavior of self-attracting particle systems with different short-range regularizations, revealing how phase transitions evolve with system parameters and discussing the validity of mean-field approximations.

Contribution

It provides a detailed phase diagram analysis for self-attracting systems with various regularizations, highlighting the transition from collapse to normal phase transitions and the role of metastable states.

Findings

Self-attracting systems exhibit collapse-like transitions with short-range regularizations.

Transition types change from first-order to second-order as parameters vary.

Metastable states and mean-field approximation validity are critically discussed.

Abstract

Phase diagram of microcanonical ensembles of self-attracting particles is studied for two types of short-range potential regularizations: self-gravitating fermions and classical particles interacting via attractive soft $-(r^2+r_0^2)^{-1/2}$ Coulomb potential. When the range of regularization is sufficiently short, the self-attracting systems exhibit gravitational or collapse-like transition. As the fermionic degeneracy or the softness radius increases, the gravitational phase transition crosses over to a normal first-order phase transition, becomes second-order at a critical point, and finally disappears. Applicability of a commonly used saddle-point or mean-field approximation and importance of metastable states is discussed.