Out-of-equilibrium phase re-entrance(s) in long-range interacting systems

TL;DR

This paper investigates out-of-equilibrium phase re-entrance phenomena in long-range interacting systems, combining Lynden-Bell's theory with N-body simulations to reveal complex re-entrant behaviors and secondary phases.

Contribution

It demonstrates the occurrence of phase re-entrances and secondary phases in long-range systems, extending Lynden-Bell's theory with numerical validation.

Findings

Confirmed phase re-entrance in predicted parameter range

Discovered secondary re-entrant phases with un-magnetized states in magnetized regions

Observed persistent magnetized states in theoretically unmagnetized regions

Abstract

Systems with long-range interactions display a short-time relaxation towards Quasi Stationary States (QSSs) whose lifetime increases with system size. The application of Lynden-Bell's theory of "violent relaxation" to the Hamiltonian Mean Field model leads to the prediction of out-of-equilibrium first and second order phase transitions between homogeneous (zero magnetization) and inhomogeneous (non-zero magnetization) QSSs, as well as an interesting phenomenon of phase re-entrances. We compare these theoretical predictions with direct $N$-body numerical simulations. We confirm the existence of phase re-entrance in the typical parameter range predicted from Lynden-Bell's theory, but also show that the picture is more complicated than initially thought. In particular, we exhibit the existence of secondary re-entrant phases: we find un-magnetized states in the theoretically magnetized region as well as persisting magnetized states in the theoretically unmagnetized region.