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arXiv:1005.0556 · Acta Physica Polonica B

Noneqilibrium Phase Transition in Kinetic Ising Model: Absence of Tricritical behaviour in Presence of Impurities

Muktish Acharyya

Published Jan 1, 2012• 1 citation
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Abstract

The nonequilibrium dynamic phase transition, in the two dimensional site diluted kinetic Ising model in presence of an oscillating magnetic field, has been studied by Monte Carlo simulation. The projections of dynamical phase surface are drawn in the planes formed by the dilution and field amplitude and the plane formed by temperature and field amplitude. The tricritical behaviour is found to be absent in this case which was observed in the pure system.

DOI
10.5506/aphyspolb.43.2041

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The nonequilibrium dynamic phase transition, in the two dimensional site diluted kinetic Ising model in presence of an oscillating magnetic field, has been studied by Monte Carlo simulation. The projections of dynamical phase surface are drawn in the planes formed by the dilution and field amplitude and the plane formed by temperature and field amplitude. The tricritical behaviour is found to be absent in this case which was observed in the pure system.
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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 have studied the nonequilibrium dynamic phase transitions of both three-dimensional (3D) kinetic Ising and Heisenberg spin systems in the presence of a perturbative magnetic field by Monte Carlo simulation. The feature of the phase transition is characterized by studying the distribution of the dynamical order parameter. In the case of anisotropic Ising spin system (ISS), the dynamic transition is discontinuous and continuous under low and high temperatures respectively, which indicates the existence of a tri-critical point (TCP) on the phase \linebreak boundary separating low-temperature order phase and high-temperature disorder phase. The TCP shifts towards the higher temperature region with the decrease of frequency, i.e. T TCP =1.33 × exp(−ω/30.7). In the case of the isotropic Heisenberg spin system (HSS), however, the situation on dynamic phase transition of HSS is quite different from that of ISS in that no stable dynamical phase transition was observed in kinetic HSS after a threshold time. The evolution of magnetization in the HSS driven by a symmetrical external field after a certain duration always tends asymptotically to a disorder state no matter what an initial state the system starts with. The threshold time τ depends upon the amplitude H 0 , reduced temperature T / T C and the frequency ω as τ = C .ω α . H 0 −β .( T / T C ) −γ .
The dynamic phase transition has been studied in the three-dimensional kinetic Ising model in the presence of a time-varying(sinusoidal)magnetic field by Monte Carlo simulation.The nature of the transition is characterized by studying the distribution of the order parameter.The system is in contact with an isothermal heat bath at temperature T.We varied the magnitude of the magnetic field,keeping the frequency of the magnetic field unchanged.For the lower values of the environment temperature the transition is discontinuous and it is continuous for higher values of the environment temperature,indicating the existence of a tricritical point (TCP) on the phase boundary.The TCP shifts towards higher temperature region with the decrease of frequency.i.e:TTCP=1.33×e(-ω/30.7)