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physica status solidi (b)

Dynamic Response of an Ising System to a Time-Dependent Field

T. Pitzschke, Steffen Trimper

Published Feb 1, 1999• 0 citations
Publisher

Abstract

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.

DOI
10.1002/(sici)1521-3951(199902)211:2<771::aid-pssb771>3.0.co;2-i

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The Master equation of the kinetic Ising model with spin-flip and spin-exchange dynamics is written in a second quantized in terms of Pauli operators. The introduction of weighted transition rates allows a general formulation in accordance with the principle of detailed balance. Static and dynamic correlation functions are calculated. The structure factor reveals three different relaxation times already in an extended mean-field approximation. Additionally, we derive a nonlinear evolution equation for the magnetization under the influence of nonthermal external noise. Already in lowest order, the correlation function offers a stretched-exponential behavior with a universal exponent \ensuremath{\sigma}=4(d+2) below the critical dimensionality dc{\mathit{d}}_{\mathit{c}}dc​=2. A one-loop renormalization group approach is used to calculate the critical exponents for the growth of the magnetization. The value of the growth exponent \ensuremath{\beta}=2(2-d)(8+d) is supported by simulations in one dimension. \textcopyright{} 1996 The American Physical Society.
The nonequilibrium dynamic phase transition, in the kinetic Ising model in the presence of an oscillating magnetic field has been studied both by Monte Carlo simulation and by solving numerically the mean-field dynamic equation of motion for the average magnetization. In both cases, the Debye ``relaxation'' behavior of the dynamic order parameter has been observed and the ``relaxation time'' is found to diverge near the dynamic transition point. The Debye relaxation of the dynamic order parameter and the power law divergence of the relaxation time have been obtained from a very approximate solution of the mean-field dynamic equation. The temperature variation of appropriately defined ``specific heat'' is studied by the Monte Carlo simulation near the transition point. The specific heat has been observed to diverge near the dynamic transition point.
The nonequilibrium dynamic phase transition, in the kinetic Ising model in presence of an oscillating magnetic field, has been studied by Monte Carlo simulation. The fluctuation of dynamic order parameter has been studied as a function of temperature near the dynamic transition point. The temperature variation of appropriately defined `susceptibility' has also been studied near the dynamic transition point. Similarly, fluctuation of energy and appropriately defined `specific-heat' have been studied as a function of temperature near the dynamic transition point. In both the cases, the fluctuations (of dynamic order parameter and energy) and the corresponding responses diverge (as power law fashion) near the dynamic transition point with similar critical behavior (with identical exponent values).
We studied the dynamical phase transition in kinetic Ising ferromagnets driven by oscillating magnetic field in meanfield approximation. The meanfield differential equation was solved by sixth-order Runge–Kutta–Felberg method. The time-averaged magnetization plays the role of the dynamic order parameter. We studied the relaxation behavior of the dynamic order parameter close to the transition temperature, which depends on the amplitude of the applied magnetic field. We observed the critical slowing down along the dynamic phase boundary. We proposed a power law divergence of the relaxation time and estimated the exponent. We also found its dependence on the field amplitude and compared the result with the exact value in limiting case.