Non-mean-field Critical Exponent in a Mean-field Model : Dynamics versus Statistical Mechanics

Abstract

The mean-field theory tells that the classical critical exponent of susceptibility is the twice of that of magnetization. However, the linear response theory based on the Vlasov equation, which is naturally introduced by the mean-field nature, makes the former exponent half of the latter for families of quasistationary states having second order phase transitions in the Hamiltonian mean-field model and its variances. We clarify that this strange exponent is due to existence of Casimir invariants which trap the system in a quasistationary state for a time scale diverging with the system size. The theoretical prediction is numerically confirmed by $N$-body simulations for the equilibrium states and a family of quasistationary states.

6 pages, 3 figures

References in corpus (3)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Out-of-equilibrium tricritical point in a system with long-range interactions
• Spectral and formal stability criteria of spatially inhomogeneous stationary solutions to the Vlasov equation for the Hamiltonian mean-field model

Cited by in corpus (9)

• Nonlinear response for external field and perturbation in the Vlasov system
• Thermodynamics of a one-dimensional self-gravitating gas with periodic boundary conditions
• Nonstandard transitions in the Kuramoto model: A role of asymmetry in natural frequency distributions
• Low-frequency discrete breathers in long-range systems without on-site potential
• Strange Scaling and Temporal Evolution of Finite-Size Fluctuation in Thermal Equilibrium
• Conditions for predicting quasistationary states by rearrangement formula
• Non-diagonalizable and non-divergent susceptibility tensor in the Hamiltonian mean-field model with asymmetric momentum distributions
• Critical exponents in mean-field classical spin systems
• Nondivergent and negative susceptibilities around critical points of a long-range Hamiltonian system with two order parameters