Quasistationarity in a model of classical spins with long-range interactions

Abstract

Systems with long-range interactions, while relaxing towards equilibrium, sometimes get trapped in long-lived non-Boltzmann quasistationary states (QSS) which have lifetimes that grow algebraically with the system size. Such states have been observed in models of globally coupled particles that move under Hamiltonian dynamics either on a unit circle or on a unit spherical surface. Here, we address the ubiquity of QSS in long-range systems by considering a different dynamical setting. Thus, we consider an anisotropic Heisenberg model consisting of classical Heisenberg spins with mean-field interactions and evolving under classical spin dynamics. Our analysis of the corresponding Vlasov equation for time evolution of the phase space distribution shows that in a certain energy interval, relaxation of a class of initial states occurs over a timescale which grows algebraically with the system size. We support these findings by extensive numerical simulations. This work further supports the generality of occurrence of QSS in long-range systems evolving under Hamiltonian dynamics.

12 pages, 3 figures; v2: minor revision

References in corpus (11)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Long time behavior of quasi-stationary states of the Hamiltonian Mean-Field model
• Slow relaxation in long-range interacting systems with stochastic dynamics
• Hamiltonian dynamics reveals the existence of quasi-stationary states for long-range systems in contact with a reservoir
• Statistical Mechanics of Unbound Two Dimensional Self-Gravitating Systems
• Incomplete equilibrium in long-range interacting systems
• Quasi-stationary states and the range of pair interactions
• Relaxation to thermal equilibrium in the self-gravitating sheet model
• Relaxation times of unstable states in systems with long range interactions
• Microcanonical quasi-stationarity of long-range interacting systems in contact with a heat bath
• Relaxation dynamics of stochastic long-range interacting systems

Cited by in corpus (17)

• Kuramoto model of synchronization: Equilibrium and nonequilibrium aspects
• The world of long-range interactions: A bird's eye view
• Scaling of the dynamics of homogeneous states of one-dimensional long-range interacting systems
• Linear response theory for long-range interacting systems in quasistationary states
• Dynamics and physical interpretation of quasi-stationary states in systems with long-range interactions
• Secular dynamics of long-range interacting particles on a sphere in the axisymmetric limit
• Action diffusion and lifetimes of quasistationary states in the Hamiltonian Mean Field model
• Kinetic theory of $1D$ homogeneous long-range interacting systems sourced by $1/N^2$ effects
• Kinetic theory of one-dimensional homogeneous long-range interacting systems with an arbitrary potential of interaction
• Overdamped dynamics of long-range systems on a one-dimensional lattice: Dominance of the mean-field mode and phase transition
• Classical Heisenberg spins with long-range interactions: Relaxation to equilibrium for finite systems
• Lyapunov Exponent and Criticality in the Hamiltonian Mean Field Model
• Kinetic theory of one-dimensional inhomogeneous long-range interacting $N$-body systems at order $1/N^2$ without collective effects
• Non-diagonalizable and non-divergent susceptibility tensor in the Hamiltonian mean-field model with asymmetric momentum distributions
• From conformal invariance to quasistationary states
• Critical exponents in mean-field classical spin systems
• Relaxation to equilibrium in models of classical spins with long-range interactions