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

Year: 2021

Authors: Vesperini A., Franzosi R., Ruffo S., Trombettoni A., Leoncini X.

Autors Affiliation: Univ Siena, Dipartimento Sci Fis Terra & Ambiente DSFTA, Via Roma 56, I-53100 Siena, Italy; Aix Marseille Univ, Univ Toulon, CPT, CNRS, Marseille, France; QSTAR, Largo Enrico Fermi 2, I-50125 Florence, Italy; CNR Ist Nazl Ott, Largo Enrico Fermi 2, I-50125 Florence, Italy; SISSA, Via Bonomea 265, I-34136 Trieste, Italy; Ist Nazl Fis Nucl, Sez Trieste, Via Bonomea 265, I-34136 Trieste, Italy; CNR, Ist Sistemi Complessi, Via Madonna Piano 10, I-50019 Sesto Fiorentino, Italy; Univ Trieste, Dept Phys, Str Costiera 11, I-34151 Trieste, Italy; CNR IOM DEMOCRITOS Simulat Ctr, I-34136 Trieste, Italy.

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 long-lived metastable 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. (c) 2021 Elsevier Ltd. All rights reserved.

Journal/Review: CHAOS SOLITONS & FRACTALS

Volume: 153      Pages from: 111487-1  to: 111487-7

More Information: R.F. acknowledges support by the QuantERA ERA-NET Co-fund 731473 (Project Q-CLOCKS). S.R. is financially supported by the MISTI Global Seed Funds MIT-FVG Collaboration Grant NV centers for the test of the Quantum Jarzynski Equality (NVQJE), and the MIUR-PRIN2017 project Coarse-grained description for nonequilibrium systems and transport phenomena (CO-NEST) No. 201798CZL.
KeyWords: Ergodicity-breaking; Hamitonian mean-field model; Quasi-stationary state; Out-ofequilibrium; Collective structure; Long-range interaction
DOI: 10.1016/j.chaos.2021.111487

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