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arXiv:cond-mat/9803127 · Physical Review Letters

Kinetic Ising Model in an Oscillating Field: Finite-Size Scaling at the Dynamic Phase Transition

Scott Sides, Per Arne Rikvold, M. A. Novotny

Published Jul 27, 1998• 227 citations
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Abstract

We study hysteresis for a two-dimensional spin- $1/2$ nearest-neighbor kinetic Ising ferromagnet in an oscillating field using Monte Carlo simulations. The period-averaged magnetization is the order parameter for a proposed dynamic phase transition (DPT). To quantify the nature of this transition, we present the first finite-size scaling study of the DPT for this model. Evidence of a diverging correlation length is given, and we provide estimates of the transition frequency and the critical indices $\ensuremath{\beta}$, $\ensuremath{\gamma}$, and $\ensuremath{\nu}$.

DOI
10.1103/physrevlett.81.834

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The two-dimensional kinetic Ising model, when exposed to an oscillating applied magnetic field, has been shown to exhibit a nonequilibrium, second-order dynamic phase transition (DPT), whose order parameter Q is the period-averaged magnetization. It has been established that this DPT falls in the same universality class as the equilibrium phase transition in the two-dimensional Ising model in zero applied field. Here we study the scaling of the dynamic order parameter with respect to a nonzero, period-averaged, magnetic "bias" field, H(b) for a DPT produced by a square-wave applied field. We find evidence that the scaling exponent, delta(d), of H(b) at the critical period of the DPT is equal to the exponent for the critical isotherm, delta(e), in the equilibrium Ising model. This implies that H(b) is a significant component of the field conjugate to Q. A finite-size scaling analysis of the dynamic order parameter above the critical period provides further support for this result. We also demonstrate numerically that, for a range of periods and values of H(b) in the critical region, a fluctuation-dissipation relation (FDR), with an effective temperature T(eff)(T,P,H0) depending on the period, and possibly the temperature and field amplitude, holds for the variables Q and H(b). This FDR justifies the use of the scaled variance of Q as a proxy for the nonequilibrium susceptibility, partial differential Q/partial differential H(b), in the critical region.
Using Monte Carlo simulations based on the Metropolis algorithm, we investigate the dynamic phase transition properties of kinetic Ising model driven by a sinusoidally oscillating magnetic field in the presence of additive white noise. We calculate equilibrium and dynamic properties such as the temperature dependence of average magnetization and magnetic specific heat, as well as the period dependence of dynamic order parameter and scaled variance. After determining the critical period at which order-disorder transition takes place, we perform finite size scaling analysis to extract the exponent ratios, and discuss the variation of these properties in the presence of noisy magnetic field. As a general result, we show that for a noisy system, DPT does not fall into a universality class of the conventional dynamic (and also equilibrium) universality class of the Ising model.
The dynamic phase transition (DPT) temperatures and the dynamic phase diagrams are obtained for spin-1/2 Ising system under the presence of a time-dependent oscillating external magnetic field using the method that was purposed by Meijer and Edwards [ANNALS of PHYSICS, 54, 240 (1969)] within the framework of the Bethe or constant coupling theory. The time variation of magnetization is investigated to find the phases in the system. Thermal behavior of the average magnetization is studied to characterize the nature (continuous and discontinuous) of transitions and to obtain the dynamic phase transition temperatures. The DPT temperatures are found always a second-order; hence there can be no tricritical point separating lines of first- and second-order dynamic phase transitions. This result agrees with the dynamic Monte-Carlo (MC) simulations of a two-dimensional kinetic spin-1/2 Ising model in an oscillating external magnetic field.
Abstract The ferromagnet to paramagnet phase transition temperature depends on the dilution concentration in the site diluted Ising ferromagnet. Though this model is a bistable system, few studies reported dynamic phase transition (DPT) in diluted Ising ferromagnet. We study dilution-dependent DPT in diluted Ising ferromagnet via Monte Carlo simulation under a time-varying external field tuning the system’s temperature on several system sizes. The nature of the transition is characterized by employing the finite-size scaling study.
We perform extensive Monte Carlo simulations to investigate the dynamic phase transition properties of the two-dimensional kinetic Ising model on the kagome lattice in the presence of square-wave oscillating magnetic field. Through detailed finite-size scaling analysis, we study universality aspects of the nonequilibrium phase transition. Obtained critical exponents indicate that the two-dimensional kagome-lattice kinetic Ising model belongs to the same universality class with the corresponding Ising model in equilibrium. Moreover, dynamic critical exponent of the local moves used in simulations is determined with high precision. Our numerical results are compatible with the previous ones on kinetic Ising models.