Fast collective oscillations and clustering phenomena in an antiferromagnetic mean-field model

TL;DR

This paper investigates the out-of-equilibrium dynamics of an antiferromagnetic mean-field model, revealing collective oscillations and clustering phenomena that are not predicted by traditional equilibrium statistical mechanics.

Contribution

It introduces a low-energy approximation and a self-consistent theory explaining the formation of biclusters and collective oscillations in the model.

Findings

Identification of a stationary bicluster state at low energy

Derivation of explicit magnetization dynamics showing coherent oscillations

Discovery of bimodal and quadrimodal phase distributions for the magnetization

Abstract

We study the out-of-equilibrium properties of the antiferromagnetic Hamiltonian Mean-Field model at low energy. In this regime, the Hamiltonian dynamics exhibits the presence of a stationary state where the rotators are gathered in a bicluster. This state is not predicted by equilibrium statistical mechanics in the microcanonical ensemble. Performing a low kinetic energy approximation, we derive the explicit expression of the magnetization vector as a function of time. We find that the latter displays coherent oscillations, and we show numerically that the probability distribution for its phase is bimodal or quadrimodal. We then look at the individual rotator dynamics as a motion in an external time-dependent potential, given by the magnetization. This dynamics exhibits two distinct time scales, with the fast one associated to the oscillations of the global magnetization vector. Performing an average over the fast oscillations, we derive an expression for the effective force acting on the individual rotator. This force is always bimodal, and determines a low frequency oscillation of the rotators. Our approach leads to a self-consistent theory linking the time-dependence of the magnetization to the motion of the rotators, providing a heuristic explanation for the formation of the bicluster.