Unveiling the nature of out-of-equilibrium phase transitions in a system with long-range interactionsM.-C. Firpo
Laboratoire de Physique des Plasmas, CNRS-Ecole Polytechnique - 91128 Palaiseau cedex, France, EU
received 19 May 2009; accepted in final form 16 October 2009; published November 2009
published online 17 November 2009
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 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.
05.70.Fh - Phase transitions: general studies.
05.45.-a - Nonlinear dynamics and chaos.
05.20.Dd - Kinetic theory.
© EPLA 2009