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Phase Transitions

Dynamic phase transition in the kinetic spin-5/2 Blume–Emery–Griffiths model in an oscillating external magnetic field

Mustafa Keskín, Mehmet Ertaş

Published May 1, 2010• 10 citations
Publisher

Abstract

Employing a mean-field approach, we study the stationary states of the kinetic spin-5/2 Blume–Emery–Griffiths (BEG) model under the presence of a time-varying (sinusoidal) magnetic field by using the Glauber-type stochastic dynamics. We employ the Glauber transition rates to construct the set of dynamic mean-field equations. We investigate the time variation in average order parameters to find the phases in the system, and the thermal behavior of the dynamic order parameters to characterize the nature (continuous or discontinuous) of the dynamic phase transtions and to the dynamic phase transition temperature. The dynamic phase diagrams are presented in three different planes. The phase diagrams contain the ferromagnetic-5/2, the ferromagnetic-3/2, the ferromagnetic-1/2, the ferroquadrupolar, and disordered fundamental phases. They also include the nine coexisting or mixed phases composed of binary and ternary combinations of fundamental phases that strongly depend on the interaction parameters. The phase diagrams display the critical end point, double critical end point, triple point, quadruple point, and one, two, or three special points and the dynamic tricritical point that depends on the interaction parameters.

DOI
10.1080/01411591003722336

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Employing a mean-field approach, we study the stationary states of the kinetic spin-5/2 Blume–Emery–Griffiths (BEG) model under the presence of a time-varying (sinusoidal) magnetic field by using the Glauber-type stochastic dynamics. We employ the Glauber transition rates to construct the set of dynamic mean-field equations. We investigate the time variation in average order parameters to find the phases in the system, and the thermal behavior of the dynamic order parameters to characterize the nature (continuous or discontinuous) of the dynamic phase transtions and to the dynamic phase transition temperature. The dynamic phase diagrams are presented in three different planes. The phase diagrams contain the ferromagnetic-5/2, the ferromagnetic-3/2, the ferromagnetic-1/2, the ferroquadrupolar, and disordered fundamental phases. They also include the nine coexisting or mixed phases composed of binary and ternary combinations of fundamental phases that strongly depend on the interaction parameters. The phase diagrams display the critical end point, double critical end point, triple point, quadruple point, and one, two, or three special points and the dynamic tricritical point that depends on the interaction parameters.
The dynamic phase transitions are studied, within a mean-field approach, in the kinetic Blume–Emery–Griffiths model under the presence of a time varying (sinusoidal) magnetic field by using the Glauber-type stochastic dynamics. The behaviour of the time-dependence of the order parameters and the behaviour of the average order parameters in a period, which is also called the dynamic order parameters, as a function of reduced temperature, are investigated. The nature (continuous and discontinuous) of transition is characterized by studying the average order parameters in a period. The dynamic phase transition points are obtained and the phase diagrams are presented in the reduced magnetic field amplitude and reduced temperature plane. The phase diagrams exhibit one, two, or three dynamic tricritical points and a dynamic double critical end point, and besides a disordered and two ordered phases, seven coexistence phase regions exist, which strongly depend on interaction parameters. We also calculate the Liapunov exponent to verify the stability of solutions and the dynamic phase transition points.
Abstract We study, within a mean-field approach, the stationary states of the kinetic metamagnetic spin −3/2 Blume-Emery-Griffiths model under the presence of a time-varying (sinusoidal) magnetic field.We use the Glauber-type stochastic dynamics to describe the time evolution of the system. The behaviour of the time dependence of the average order parameters in a period, which are also called the dynamic order parameters, as functions of the reduced temperature are investigated. The natures (continuous or discontinuous) of the transitions are characterized by investigating the behaviours of the thermal variations of the dynamic order parameters. The dynamic phase transition points are obtained and the phase diagrams are constructed in the plane of the reduced temperature (T) and the amplitude of the magnetic field (h), and sixteen fundamental types of phase diagrams are found. The phase diagrams exhibit one, two, three or four dynamic tricritical points and a dynamic double-critical end point, and, besides a disordered and three ordered phases, seven coexistence regions or mixed phases depending on the interaction parameters. We also investigate the influence of the reduced biquadratic exchange parameter (k) and obtain nine different phase diagram topologies in the (k,T) plane
We calculate the dynamic phase transition (DPT) temperatures and present the dynamic phase diagrams in the kinetic spin-5/2 Blume–Capel model under the presence of a time-dependent oscillating external magnetic field. First, we employ the Glauber transition rates to construct the mean-field dynamic equation. Then, we study the time variation of the average magnetization to find the phases in the system. We also investigate the behaviour of the dynamic magnetization to characterize the nature (continuous and discontinuous) of transition and to obtain the DPT points. We present the dynamic phase diagrams in two different planes. The phase diagrams include the ferromagnetic-5/2 (f5/2), the ferromagnetic-1/2 (f1/2) and paramagnetic (p) fundamental phases. In addition to these fundamental phases, we find 10 mixed phases, depending on the interaction parameters. The phase diagrams display many special points, such as a dynamic tricritical point, a double critical end point, a triple point and a quadruple point.
Within a mean-field approach and using the Glauber-type stochastic dynamics, we study the kinetics of the spin-2 Blume-Capel model in the presence of a time-varying (sinusoidal) magnetic field. We investigate the time dependence of the average order parameter and the behavior of the average order parameter in a period, which is also called the dynamic order parameter, as a function of the reduced temperature. The nature (continuous and discontinuous) of the transition is characterized by the dynamic order parameter. The dynamic phase transition points are obtained and the phase diagrams are presented in the reduced magnetic field amplitude and reduced temperature plane. The phase diagrams exhibit one dynamic tricritical point; besides a disordered and an ordered phases, there are three phase coexistence regions that are strongly dependent on the interaction parameter.
We calculate the dynamic phase transition (DPT) temperatures and present the dynamic phase diagrams in the kinetic mixed spin-1/2 and spin-5/2 Ising model under the presence of a time-dependent oscillating external magnetic field. We employ the Glauber transition rates to construct the set of mean-field dynamic equations. The time variation of the average magnetizations and the thermal behavior of the dynamic magnetizations are investigated, extensively. The nature (continuous or discontinuous) of the transitions is characterized by studying the thermal behaviors of the dynamic magnetizations. The DPT points are obtained and the phase diagrams are presented in two different planes. Phase diagrams contain four fundamental phases and three coexistence or mixed phases, which strongly depend on interaction parameters. The phase diagrams are discussed and a comparison is made with the results of the other mixed spin Ising systems.
The dynamic magnetic behavior of the kinetic metamagnetic spin-5/2 Blume—Capel model is examined, within a mean-field approach, under a time-dependent oscillating magnetic field. To describe the kinetics of the system, Glauber-type stochastic dynamics has been utilized. The mean-field dynamic equations of the model are obtained from the Master equation. Firstly, these dynamic equations are solved to find the phases in the system. Then, the dynamic phase transition temperatures are obtained by investigating the thermal behavior of dynamic sublattice magnetizations. Moreover, from this investigation, the nature of the phase transitions (first- or second-order) is characterized. Finally, the dynamic phase diagrams are plotted in five different planes. It is found that the dynamic phase diagrams contain the paramagnetic (P), antiferromagnetic (AF 5/2 , AF 3/2 , AF 1/2 ) phases and five different mixed phases. The phase diagrams also display many dynamic critical points, such as tricritical point, triple point, quadruple point, double critical end point and separating point.