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

TL;DR

This paper demonstrates that classical spins with long-range interactions can exhibit quasistationary states (QSS) that persist for timescales increasing algebraically with system size, extending the understanding of QSS beyond particle models.

Contribution

It introduces a new dynamical setting for QSS by analyzing an anisotropic Heisenberg model with mean-field interactions and classical spin dynamics.

Findings

QSS occur in the Heisenberg spin model within a specific energy range.

Relaxation times of initial states grow algebraically with system size.

Numerical simulations support the theoretical analysis of QSS in the model.

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.