Unveiling the nature of out-of-equilibrium phase transitions in a system with long-range interactions

TL;DR

This paper investigates out-of-equilibrium phase transitions in a long-range interacting system, revealing that these transitions are bifurcations between integrable and ergodic dynamics in the Vlasov limit, with implications for understanding quasistationary states.

Contribution

It introduces a new theoretical framework linking out-of-equilibrium phase transitions to bifurcations in Vlasov dynamics, explaining the nature of observed QSS phase transitions.

Findings

Out-of-equilibrium phase transitions are bifurcations in Vlasov dynamics.

Time-asymptotic states relate to simple force field forms.

Magnetization behavior at phase transition supports the bifurcation picture.

Abstract

Recently, there has been some vigorous interest in the out-of-equilibrium quasistationary states (QSSs), with lifetimes diverging with the number N of degrees of freedom, emerging from numerical simulations of the ferromagnetic XY Hamiltonian Mean Field (HMF) starting from some special initial conditions. Phase transitions have been reported between low-energy magnetized QSSs and large-energy unexpected, antiferromagnetic-like, QSSs with low magnetization. This issue is addressed here in the Vlasov N \rightarrow \infty limit. It is argued that the time-asymptotic states emerging in the Vlasov limit can be related to simple generic time-asymptotic forms for the force field. The proposed picture unveils the nature of the out-of-equilibrium phase transitions reported for the ferromagnetic HMF: this is a bifurcation point connecting an effective integrable Vlasov one-particle time-asymptotic dynamics to a partly ergodic one which means a brutal open-up of the Vlasov one-particle phase space. Illustration is given by investigating the time-asymptotic value of the magnetization at the phase transition, under the assumption of a sufficiently rapid time-asymptotic decay of the transient force field.