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arXiv:1303.3702

Time dependent magnetic field effects on the $\pm J$ Ising model

Erol Vatansever, Ümit Akıncı, Hamza Polat

Published Mar 15, 2013• 0 citations
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Abstract

Nonequilibrium phase transition properties of the $\pm J$ 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.

DOI
10.48550/arxiv.1303.3702

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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.
Nonequilibrium magnetic properties in a two-dimensional kinetic mixed spin-2 and spin-5/2 Ising system in the presence of a time-varying (sinusoidal) magnetic field are studied within the effective-field theory (EFT) with correlations. The time evolution of the system is described by using Glauber-type stochastic dynamics. The dynamic EFT equations are derived by employing the Glauber transition rates for two interpenetrating square lattices. We investigate the time dependence of the magnetizations for different interaction parameter values in order to find the phases in the system. We also study the thermal behavior of the dynamic magnetizations, the hysteresis loop area, and dynamic correlation. The dynamic phase diagrams are presented in the reduced magnetic field amplitude and reduced temperature plane and we observe that the system exhibits dynamic tricritical and reentrant behaviors. Moreover, the system also displays a double critical end point (B), a zero-temperature critical point (Z), a critical end point (E), and a triple point (TP). We also performed a comparison with the mean-field prediction in order to point out the effects of correlations and found that some of the dynamic first-order phase lines, which are artifacts of the mean-field approach, disappeared.
We investigated the dynamical behavior of an Ising model in a square lattice subject to a time-dependent external magnetic field. In our model the exchange coupling between first neighboring spins in the horizontal direction is different from that of the vertical direction. We have employed the master equation approach for the Glauber stochastic process and used the dynamical pair approximation in order to decouple the hierarchy of equations. We have found the stationary phase diagram for this model in the plane amplitude of the oscillating field versus temperature, for different values of the frequency of the external field and of the ratio between the vertical and the horizontal couplings. Depending on these values, the phase diagram can exhibit the ferromagnetic, paramagnetic, and antiferromagnetic phases. The transition between these phases can be continuous or discontinuous, and the model may also display a tricritical behavior.
The phase diagram of an antiferromagnetic Ising model in a square lattice is studied as a function of temperature and of the frequency of an external uniform oscillating field. The time evolution of the staggered magnetization is obtained through the formalism of the master equation within the dynamical pair approximation. We have shown that the stationary solutions lead to transitions between the antiferromagnetic and paramagnetic phases. The critical field of the transition depends on the competition between the frequencies of the field and that of the spin flipping. We show that for high values of the frequency of the oscillating field the system remains always in a stationary antiferromagnetic state.
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.
We present a study, within a mean-field approach, of the kinetics of the mixed spin-1 and spin-3/2 Ising model Hamiltonian with bilinear and biquadratic nearest-neighbor exchange interactions and a single-ion potential or crystal-field interaction in the presence of a time-dependent oscillating external magnetic field. We employ the Glauber transition rates to construct the mean-field dynamical equations. We investigate the time dependence of average magnetizations and the quadrupole moments, and the thermal behavior of the dynamic order parameters. From these studies, we obtain the dynamic phase transition (DPT) points and construct the phase diagrams in three different planes. Phase diagrams contain disordered (d) , ferrimagnetic (i) , the antiquadrupolar or staggered (a) phases, and four coexistence or mixed phase regions, namely, the i+d , i+a , i+a+d , and a+d , that strongly depend on interaction parameters. The system also exhibits the dynamic tricritical behavior in most cases, the reentrant behavior in few cases.
Using the mean-field theory and Glauber-type stochastic dynamics, we study the dynamic magnetic properties of the mixed spin (2, 5/2) Ising system for the antiferromagnetic/antiferromagnetic (AFM/AFM) interactions on the bilayer square lattice under a time varying (sinusoidal) magnetic field. The time dependence of average magnetizations and the thermal variation of the dynamic magnetizations are examined to calculate the dynamic phase diagrams. The dynamic phase diagrams are presented in the reduced temperature and magnetic field amplitude plane and the effects of interlayer coupling interaction on the critical behavior of the system are investigated. We also investigate the influence of the frequency and find that the system displays richer dynamic critical behavior for higher values of frequency than that of the lower values of it. We perform a comparison with the ferromagnetic/ferromagnetic (FM/FM) and AFM/FM interactions in order to see the effects of AFM/AFM interaction and observe that the system displays richer and more interesting dynamic critical behaviors for the AFM/AFM interaction than those for the FM/FM and AFM/FM interactions.