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

TL;DR

This study explores how temporal modulation of the coupling matrix in the Hamiltonian mean-field model affects phase transition points and the persistence of quasi-stationary states, revealing that amplitude influences the critical shift more than frequency.

Contribution

It introduces a numerical analysis of the HMF model with a time-dependent coupling matrix, highlighting the effects of modulation amplitude and frequency on phase transition and QSS.

Findings

Critical point shifts due to temporal modulation.

Shift is independent of frequency above a threshold.

QSS persists despite coupling modulation.

Abstract

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.