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

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.

References in corpus (8)

• Out-of-equilibrium tricritical point in a system with long-range interactions
• Abundance of regular orbits and out-of-equilibrium phase transitions in the thermodynamic limit for long-range systems
• Dynamical phase transitions in long-range Hamiltonian systems and Tsallis distributions with a time-dependent index
• Lynden-Bell and Tsallis distributions for the HMF model
• Relaxation times of unstable states in systems with long range interactions
• Ergodicity and Central Limit Theorem in Systems with Long-Range Interactions
• Out of Equilibrium Solutions in the $XY$-Hamiltonian Mean Field model
• Algebraic Correlation Function and Anomalous Diffusion in the HMF model

Cited by in corpus (1)

• Emergence of a non trivial fluctuating phase in the XY model on regular networks