Hamiltonian mean field model : effect of temporal perturbation in coupling matrix

The Hamiltonian mean-field (HMF) model is a system of fully coupled rotators which exhibits a second-order phase transition at some critical energy in its canonical ensemble. We investigate the case where the interaction between the rotors is governed by a time-dependent coupling matrix. Our numeric...

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Bibliographic Details
Published in:arXiv.org 2018-05
Main Authors: Bhadra, Nivedita, Patra, Soumen K
Format: Article
Language:English
Subjects:
Coupling
Critical point
Mathematical models
Modulation
Perturbation methods
Phase transitions
Rotors
Time dependence
Online Access:Get full text
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Summary:The Hamiltonian mean-field (HMF) model is a system of fully coupled rotators which exhibits a second-order phase transition at some critical energy in its canonical ensemble. We investigate the case where the interaction between the rotors is governed by a time-dependent coupling matrix. Our numerical study reveals a shift in the critical point due to the temporal modulation. The shift in the critical point is shown to be independent of the modulation frequency above some threshold value, whereas the impact of the amplitude of modulation is dominant. In the microcanonical ensemble, the system with constant coupling reaches a quasi-stationary state (QSS) at an energy near the critical point. Our result indicates that the QSS subsists in presence of such temporal modulation of the coupling parameter.
ISSN:2331-8422
DOI:10.48550/arxiv.1710.09633