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Journal of Physics D Applied Physics

Dynamic phase transition in classical Ising models

Yusuf Yüksel, Erol Vatansever

Published Oct 13, 2021• 20 citations
Publisher

Abstract

Abstract When a ferromagnetic system is driven by an oscillating magnetic field, the system shows various intriguing magnetic properties. The two most common features are dynamic phase transition and dynamic hysteresis resulting from the competition between the period of the external field and the metastable lifetime of the system. In this article, we mainly review the similarities and dissimilarities between ferromagnetic systems in thermal equilibrium and those exposed to a driving time-dependent magnetic field. Extensive studies performed over two decades have shown that dynamic and thermodynamic phase transitions correspond to the same universality class and have similar phase diagrams, among other similarities. Remarkably, recent experimental studies have revealed that both fluctuations in dynamic order parameter and susceptibility can demonstrate anomalously sharp sidebands, which are known as metamagnetic anomalies, in the dynamically paramagnetic phase close to the critical point. This behavior is one of the most interesting behaviors observed in the magnetic systems driven by a time-dependent field which does not have an analog in the corresponding equilibrium counterparts. We discuss the general picture regarding the effects of the applied field components on the metamagnetic anomalies. As a main conclusion, we remark that a comprehensive literature overview reveals that the similarities between conventional thermodynamic phase transitions and corresponding dynamic counterpart are only limited to the vicinity of critical period regime with zero bias field, and they should be treated very carefully in the presence of surfaces. Finally, some of the main questions waiting to be answered and potential future research directions are underlined.

DOI
10.1088/1361-6463/ac2f6c

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Abstract When a ferromagnetic system is driven by an oscillating magnetic field, the system shows various intriguing magnetic properties. The two most common features are dynamic phase transition and dynamic hysteresis resulting from the competition between the period of the external field and the metastable lifetime of the system. In this article, we mainly review the similarities and dissimilarities between ferromagnetic systems in thermal equilibrium and those exposed to a driving time-dependent magnetic field. Extensive studies performed over two decades have shown that dynamic and thermodynamic phase transitions correspond to the same universality class and have similar phase diagrams, among other similarities. Remarkably, recent experimental studies have revealed that both fluctuations in dynamic order parameter and susceptibility can demonstrate anomalously sharp sidebands, which are known as metamagnetic anomalies, in the dynamically paramagnetic phase close to the critical point. This behavior is one of the most interesting behaviors observed in the magnetic systems driven by a time-dependent field which does not have an analog in the corresponding equilibrium counterparts. We discuss the general picture regarding the effects of the applied field components on the metamagnetic anomalies. As a main conclusion, we remark that a comprehensive literature overview reveals that the similarities between conventional thermodynamic phase transitions and corresponding dynamic counterpart are only limited to the vicinity of critical period regime with zero bias field, and they should be treated very carefully in the presence of surfaces. Finally, some of the main questions waiting to be answered and potential future research directions are underlined.
Abstract Being inspired by the results of recent experimental work ‘Phys. Rev. E 102 022 804’, we perform a series of Monte Carlo simulations to investigate the dynamic critical properties of a binary magnetic alloy system composed of two different components with different spin moments with the chemical formula A ( p A ) B ( 1 − p A ) . In the first part of the work, we concentrate our attention on the similarities between dynamic critical behavior and thermodynamic phase transition properties of the model. Finite-size scaling analyses suggest that the proposed binary alloy model exhibits 2D Ising universality class. In the second part, we examine the dynamic critical behavior in the presence of a magnetic bias field for which a metamagnetic sideband behavior originates in dynamic susceptibility curves. Our results yield that these metamagnetic anomalies survive for a wide range of magnetic atom concentration p A , and the strength of the anomalies observed in the field-dependent dynamic susceptibility varies very slowly with the T/T c ratio of the binary magnetic alloy.
We employ numerical simulations and finite-size scaling techniques to investigate the properties of the dynamic phase transition that is encountered in the Blume-Capel model subjected to a periodically oscillating magnetic field. We mainly focus on the study of the two-dimensional system for various values of the crystal-field coupling in the second-order transition regime. Our results indicate that the present nonequilibrium phase transition belongs to the universality class of the equilibrium Ising model and allow us to construct a dynamic phase diagram, in analogy with the equilibrium case, at least for the range of parameters considered. Finally, we present some complementary results for the three-dimensional model, where again the obtained estimates for the critical exponents fall into the universality class of the corresponding three-dimensional equilibrium Ising ferromagnet.
We study the critical dynamics arising from a time-dependent periodic homogenous source coupled to the order-parameter field, which drives a classical ferromagnetic system across a continuous transition. For this purpose, we consider the paradigmatic two-dimensional (2D) Ising model in the presence of a periodic magnetic field h(t)=−A cos⁡(2πt/P)h(t)=-A\, \cos (2πt/P)h(t)=−Acos(2πt/P), evolving under a purely relaxational dynamics at the critical temperature. We show that the periodic driving gives rise to a peculiar dynamic scaling behavior in the thermodynamic limit, arising from a nontrivial interplay among the time ttt, the amplitude AAA and period PPP of h(t)h(t)h(t). The relevant scaling variables are τ=t/Pτ=t/Pτ=t/P and σ=APκσ=A P^κσ=APκ, with κ=yh/zκ= y_h/zκ=yh​/z, where yh=(d+2−η)/2y_h=(d+2-η)/2yh​=(d+2−η)/2 is the critical dimension of the magnetic field, and zzz is dynamic exponent for the critical relaxational dynamics (κ≈0.865κ\approx 0.865κ≈0.865 for the 2D Ising model). The dynamic scaling behaviors of the magnetization and bond-energy density show an oscillatory behavior around a smooth curve which approaches a large-τττ stationary behavior. We also briefly discuss the dynamic behavior of an Ising system driven across the critical point by a periodic time-varying temperature at zero magnetic field.
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.
Among the many non-equilibrium processes encountered in nature we deal with two different but related aspects. One is the non-equilibrium relaxation process that is at the origin of \'aging phenomena••, and the other one is a non-equilibrium phase transition, called ••dynamic phase transition••. One of the main purposes of our research is to explore more realistic situations than studied previously. Indeed, in the study of aging phenomena certain kinds of disorder effects are considered, and we introduce the ••surface•• as a spatial boundary to the system undergoing the dynamic phase transition. In order to observe these processes as clearly as possible, we study in both cases simple spin systems. Using Monte Carlo simulations we first investigate aging in three-dimensional Ising spin glasses as well as in two-dimensional Ising models with disorder quenched to low temperatures. The time-dependent dynamical correlation length L(t) is determined numerically and the scaling behavior of various two-time quantities as a function of L(t)/L(s) is discussed where t and s are two different times. For disordered Ising models deviations of L(t) from algebraic growth law show up. The generalized scaling forms as a function of L(t)/L(s) reveal a generic simple aging scenario for Ising spin glasses as well as for disordered Ising ferromagnets. We also study the local critical phenomena at a dynamic phase transition by means of numerical simulations of kinetic Ising models with surfaces subjected to a periodic oscillating field. We examine layer-dependent quantities, such as the period-averaged magnetization per layer Q(z) and the layer susceptibility ¥ö(z), and determine local critical exponents through finite size scaling. Both for two and three dimensions, we find that the values of the surface exponents differ from those of the equilibrium critical surface. It is revealed that the surface phase diagram of the non-equilibrium system is not identical to that of the equilibrium system in three dimensions.
Time dependent magnetic field effects on the ±J\pm J±J Ising model
Nonequilibrium phase transition properties of the ±J\pm J±J Ising model under a time dependent oscillating perturbation are investigated within the framework of effective field theory for a two-dimensional square lattice. After a detailed analysis, it is found that the studied system exhibits unusual and interesting behaviors such as reentrant phenomena, and the competition between ferromagnetic and antiferromagnetic exchange interactions gives rise to destruct the dynamic first order phase transitions as well as dynamic tricritical points. Furthermore, according to Néel nomenclature, the magnetization profiles have been found to obey Q-type, L-type and P-type classification schemes under certain conditions. Finally, it is observed that the treatment of critical percolation with applied field amplitude strongly depends upon the frequency of time varying external field.