Criticality in a Vlasov-Poisson system - a fermionic universality class

Abstract

A model Vlasov--Poisson system is simulated close the point of marginal stability, thus assuming only the wave-particle resonant interactions are responsible for saturation, and shown to obey the power--law scaling of a second-order phase transition. The set of critical exponents analogous to those of the Ising universality class is calculated and shown to obey the Widom and Rushbrooke scaling and Josephson's hyperscaling relations at the formal dimensionality $d=5$ below the critical point at nonzero order parameter. However, the two-point correlation function does not correspond to the propagator of Euclidean quantum field theory, which is the Gaussian model for the Ising universality class. Instead it corresponds to the propagator for the fermionic {\it vector} field and to the {\it upper critical dimensionality} $d_c=2$. This suggests criticality of collisionless Vlasov-Poisson systems as representative of the {\it universality class} of critical phenomena of {\it a fermionic} quantum field description.

10 pages, 6 figures, Submitted to Phys. Rev. E

References in corpus (5)

• Renormalization Group Calculation for the Reaction $kA\to \varnothing$
• Lyapunov instability and finite size effects in a system with long-range forces
• `Real' vs `Imaginary' Noise in Diffusion-Limited Reactions
• Amplitude Equations for Electrostatic Waves: universal singular behavior in the limit of weak instability
• Influence of Expansion on Hierarchical Structure

Cited by in corpus (5)

• Nonlinear response for external field and perturbation in the Vlasov system
• Non-mean-field Critical Exponent in a Mean-field Model : Dynamics versus Statistical Mechanics
• Scale-free vortex cascade emerging from random forcing in a strongly coupled system
• Thermodynamics of a one-dimensional self-gravitating gas with periodic boundary conditions
• Nontrapping arrest of Langmuir wave damping near the threshold amplitude