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arXiv:1812.07610 · Physica A Statistical Mechanics and its Applications

Dynamical response of the Ising model to an amplitude modulated time dependent magnetic field

Ümit Akıncı

Published May 14, 2019• 3 citations
arXivHTMLPDF
DOI
10.1016/j.physa.2019.121458

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The basic equation of a kinetic Ising model under the influence of a time dependent field is rederived applying the Fock space representation of the master equation. The nonequilibrium behaviour of the model in the presence of both a static and an oscillating magnetic field is analyzed by numerical simulations and by scaling arguments. Forcing the system to be initially in the metastable state and imposing an additional oscillating field makes it possible to study the relaxation time of this state. We find a power law behaviour for the waiting time depending on the amplitude and the frequency of the field as well as on the reduced temperature. The critical exponents are determined numerically. Furthermore, the results are supported by scaling arguments.
We study the all-to-all Ising model in the presence of dissipation and periodic external field. The corresponding Lindblad equation has a time-periodic Liouvillian. The dynamics of magnetizations is explored by using both the mean-field theory and numerical simulation at a finite number of spins. The mean-field result exhibits a transition from the periodic response at small field amplitude to the chaotic dynamics at large amplitude. The Lyapunov exponents are calculated, which supports the existence of a classical chaotic phase. However, in the numerical simulation at a finite number of spins, the response is periodic at both small and large amplitudes. The scaling analysis of the Floquet Liouvillian spectrum suggests that the periodic response persists even in the thermodynamic limit. Further analysis shows that, in the classical chaotic regime, the density-matrix elements have a wide dispersion, instead of being localized. Such a delocalization of wave packets explains the failure of mean-field approximation.