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The Hamiltonian mean-field (HMF) model is a system of fully coupled rotatorswhich exhibits a second-order phase transition at some critical energy in itscanonical ensemble. We investigate the case where the interaction between therotors is governed by a time-dependent coupling matrix. Our numerical studyreveals a shift in the critical point due to the temporal modulation. The shiftin the critical point is shown to be independent of the modulation frequencyabove some threshold value, whereas the impact of the amplitude of modulationis dominant. In the microcanonical ensemble, the system with constant couplingreaches a quasi-stationary state (QSS) at an energy near the critical point.Our result indicates that the QSS subsists in presence of such temporalmodulation of the coupling parameter.

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