Mixed-Spin Ising Model in an Oscillating Magnetic Field and Compensation Temperature

Godoy et al. (Phys. Rev. B 69, 054428, 2004) presented a study of the magnetic properties of a mixed spin (1/2,1), Ising ferrimagnetic model on a hexagonal lattice without an oscillating magnetic field. They employed dynamic mean-field calculations and Monte Carlo simulations to find the compensation point of the model and to present the phase diagrams. It has been found that the N-type compensation temperature appears only when the intrasublattice interaction between spins in the σ sublattice is ferromagnetic. Moreover, the system only undergoes a second-order phase transition. In this work, we extend the study a dynamic compensation temperature of a mixed spin-1/2 and spin-1 Ising ferrimagnetic system on a hexagonal lattice in the presence of oscillating magnetic field within the framework of dynamic mean-field calculations. We find that the system displays the N-type compensation temperature. We also calculate dynamic phase diagrams in which contain the paramagnetic, ferrimagnetic, nonmagnetic fundamental phases and two different mixed phases, depending on the interaction parameters and oscillating magnetic field. The system also exhibits tricritical and reentrant behaviors.     

Phase transition properties for the kinetic Ising model in an oscillating magnetic field

The phase transition properties for the kinetic Ising model in a sinusoidally oscillating magnetic field are investigated by means of the mean-field calculations. The integrated phase diagrams for not only the amplitude of the oscillating field versus temperature but also the frequency of the oscillating field versus temperature have been calculated respectively, in which the discontinuous and continuous transitions are observed. Meanwhile the hysteresis loops in relation to the two kinds of the phase diagrams have been analyzed systematically, and the effects of the amplitude and the frequency of the oscillating field on the hysteresis loops are illustrated.     

Dynamic phase transitions in the kinetic mixed spin-1/2 and spin-5/2 Ising model under a time-dependent oscillating magnetic field

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.     

Effects of the bond dilution on the phase diagrams of a spin-1 transverse Ising model with crystal field interaction on a honeycomb lattice

A bond diluted spin-1 Ising model with crystal and transverse field interactions is examined for honeycomb lattice by introducing an effective field approximation that takes into account the correlations between different spins that emerge when expanding the identities. The effects of the crystal field as well as the transverse field and dilution on the phase diagrams and order parameter m_z are discussed in detail. A number of interesting and unusual phenomena such as reentrant phenomena and three successive phase transitions originating from the crystal field as well as the transverse field and bond dilution have been found.     

动态外场作用下Ising自旋体系的非平衡动态相变

系统地考察了Ising自旋体系的动力学方程对三种不同性质的驱动外场（正弦波 、方波和锯齿波）的动态响应及其相应的非平衡动态相变特征.在正弦波和方波的驱动场 作用下，体系存在分别对应于低温对称破缺的铁磁有序态和高温对称顺磁无序态的动态非平衡转变，相应的动态转变相界上存在区分连续转变和非连续转变的三临界点；而锯齿波驱动 场情形下体系始终维持对称性破缺的有序态.体系动态转变表现出的上述差异与作用外场的驱动特征有关.确定了表征相应动态相变相界的临界驱动外场振幅h0C和频率 ωc、体系的温度tc, 并给予了分析讨论 关键词： Ising自旋体系 非平衡动态相变 对称性 平均场     

动力学伊辛模型在振荡外场中的成核

研究了二维的动力学伊辛模型在一个具有偏向的振荡外场中的成核过程,主要关注成核时间与外场振荡周期ω的关系．随着ω的变化,成核时间出现最小值,最小的成核时间对应的平均临界核的大小也是最小的,这表明存在一个最佳的振荡频率,相比较于一个确定的外场,它更有利于成核．同时还研究了外场的初始相位的影响．     

Effects of random-crystal-field on the kinetic Blume Capel model

The effects of random crystal field on the stationary states of the kinetic spin-1 Blume Capel model are studied using the Glauber-type stochastic dynamics under the time-dependent oscillating field assumption. Our investigation, based on the equilibrium ground state phase diagram, revealed many interesting phenomena. The known phases, in the equilibrium case, are obtained for high field and are represented by limit cycles. The phase diagram of the pure pure kinetic Ising spin- and spin-1 Blume Capel models are deduced as particular cases. First-order, second-order transition lines, dynamical critical and dynamical double critical end points are also obtained.     

Effective field investigation of dynamic phase transitions for site diluted Ising ferromagnets driven by a periodically oscillating magnetic field

Dynamic behavior of a site diluted Ising ferromagnet in the presence of a periodically oscillating magnetic field has been analyzed by means of the effective field theory (EFT). The dynamic equation of motion has been solved for a honeycomb lattice (z=3$z=3$) with the help of a Glauber type stochastic process. The global phase diagrams and the variation of the corresponding dynamic order parameter as a function of the Hamiltonian parameters and temperature has been investigated in detail and it has been shown that the system exhibits reentrant phenomena, as well as a dynamic tricritical point which disappears for sufficiently weak dilution.     

Kinetic Ising model in a time-dependent oscillating external magnetic field: effective-field theory

Recently,Shi et al.[2008 Phys.Lett.A 372 5922] have studied the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field and presented the dynamic phase diagrams by using an effective-field theory(EFT) and a mean-field theory(MFT).The MFT results are in conflict with those of the earlier work of Tom’e and de Oliveira,[1990 Phys.Rev.A 41 4251].We calculate the dynamic phase diagrams and find that our results are similar to those of the earlier work of Tom’e and de Oliveira;hence the dynamic phase diagrams calculated by Shi et al.are incomplete within both theories,except the low values of frequencies for the MFT calculation.We also investigate the influence of external field frequency(ω) and static external field amplitude(h0) for both MFT and EFT calculations.We find that the behaviour of the system strongly depends on the values of ω and h0.     

Dynamic phase transitions in a cylindrical Ising nanowire under a time-dependent oscillating magnetic field

The dynamic phase transitions in a cylindrical Ising nanowire system under a time-dependent oscillating external magnetic field for both ferromagnetic and antiferromagnetic interactions are investigated within the effective-field theory with correlations and the Glauber-type stochastic dynamics approach. The effective-field dynamic equations for the average longitudinal magnetizations on the surface shell and core are derived by employing the Glauber transition rates. Temperature dependence of the dynamic magnetizations, the dynamic total magnetization, the hysteresis loop areas and the dynamic correlations are investigated in order to characterize the nature (first- or second-order) of the dynamic transitions as well as the dynamic phase transition temperatures and the compensation behaviors. The system strongly affected by the surface situations. Some characteristic phenomena are found depending on the ratio of the physical parameters in the surface shell and the core. According to the values of Hamiltonian parameters, five different types of compensation behaviors in the Néel classification nomenclature exist in the system. The system also exhibits a reentrant behavior.     

Dynamic magnetic properties of Ising graphene-like monolayer

Dynamic magnetic properties of the mixed-spin (3/2, 5/2) Ising graphene-like monolayer in an oscillating magnetic field are studied by means of Monte Carlo simulation. The effects of Hamiltonian parameters such as crystal field and time-dependent oscillating magnetic field on the dynamic order parameter, susceptibility and internal energy of the system are well presented and explained. Moreover, much attention has also been dedicated to the phase diagrams with different parameters in order to better comprehend the impacts of these parameters on the critical temperature. Our results reveal that the crystal fields of two sublattices have similar effects on the critical temperature, but the bias field and amplitude of oscillating field have opposite effects on it. We hope that our research can be of guiding significance to the theoretical and experimental studies of graphene-like monolayer.     

Stability of interfaces in a random environment. A rigorous renormalization group analysis of a hierarchical model

We study a hierarchical model of domain walls in aD-dimensional bond disordered Ising model at low temperatures. Using a renormalization group method inspired by the work of Bricmont and Kupiainen for the random field Ising model, we prove the existence of rigid interfaces at low enough temperatures in dimensionsD>3.     

Effective-field theory on the kinetic Ising model

As an analytical method, the effective-field theory (EFT) is used to study the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field. The effective-field equations of motion of the average magnetization are given for the square lattice (Z=4) and the simple cubic lattice (Z=6), respectively. The dynamic order parameter, the hysteresis loop area and the dynamic correlation are calculated. In the field amplitude h₀/ZJ-temperature T/ZJ plane, the phase boundary separating the dynamic ordered and the disordered phase has been drawn, and the dynamical tricritical point has been observed. We also make the compare results of EFT with that given by using the mean field theory (MFT).     

Effects of the Quenched Random Crystal Field on the Dynamic Spin-1 Blume-Capel Model

In this study, we have analyzed the dynamical phase transitions of spin-1 Blume-Capel model with quenched random crystal field under the effect of a time dependent oscillating magnetic field. We have obtained the magnetic field, temperature (h,T) cross sections of the global phase diagram for constant values of the concentration and the amplitude of the single-ion anisotropy within mean field approximation. There are regions of the phase space where both ordered and disordered phases coexist. In addition, the dynamic phase transition from one regime to the other can be a first- or a second-order depending on the region in the phase diagram. Hence, the system exhibits a number of interesting phenomena and a rich variety of phase diagrams with type being according to the concentration p of active local crystal fields.     

Dynamic hysteresis loops of the spin-2 bilayer Ising model

Based on the mean-field theory and Glauber-type stochastic dynamics, the dynamic hysteresis loops (DHLs) of the spin-2 Ising model are studied on the bilayer square lattice. The DHLs are given for different values of temperature, crystal-field, exchange interaction and oscillating field frequency. It is found that the physical parameters have a strong effect on the shape and number of the DHLs. The results are compared with some theoretical and experimental works and found in a qualitatively good agreement.     

Phase diagrams in an ultra-thin spin-1 transverse Ising film with bond or site dilution at surfaces

The phase diagrams of two nanoscaled thin films with bond and site dilutions at the surfaces, described by the spin-1 transverse Ising model, are investigated by the use of an effective field theory with correlations. A number of characteristic phenomena have been found in them, which are heavily dependent on the ratios (r = J₁/J and p = Ω_S/Ω, where J is the exchange interaction in the inner layer, J₁ is the exchange interaction between the surface and the next inner layer, Ω_S is the transverse field at the surfaces and Ω is the transverse field in the inner layer). Some of them have exhibited very similar behaviors found in the two spin-1/2 nanoscaled thin films with bond and site dilutions at the surfaces.     

Dynamic Dipole and Quadrupole Phase Transitions in the Kinetic Spin-3/2 Model

The dynamic phase transition has been studied, within a mean-field approach, in the kinetic spin-3/2 Ising model Hamiltonian with arbitrary bilinear and biquadratic pair interactions in the presence of a time dependent oscillating magnetic field by using the Glauber-type stochastic dynamics. The nature (first- or second-order) of the transition is characterized by investigating the behavior of the thermal variation of the dynamic order parameters and as well as by using the Liapunov exponents. The dynamic phase transitions (DPTs) are obtained and the phase diagrams are constructed in the temperature and magnetic field amplitude plane and found nine fundamental types of phase diagrams. Phase diagrams exhibit one, two or three dynamic tricritical points, and besides a disordered (D) and the ferromagnetic-3/2 (F_3/2) phases, six coexistence phase regions, namely F _3/2+ F _1/2, F _3/2+ D, F _3/2+ F _1/2+ FQ, F _3/2+ FQ, F _3/2+ FQ + D and FQ + D, exist in which depending on the biquadratic interaction. PACS number(s): 05.50.+q, 05.70.Fh, 64.60.Ht, 75.10.Hk     

Dynamic compensation temperature in kinetic spin-5/2 Ising model on hexagonal lattice

We present a study of the dynamic behavior of a two-sublattice spin-5/2 Ising model with bilinear and crystal-field interactions in the presence of a time-dependent oscillating external magnetic field on alternate layers of a hexagonal lattice by using the Glauber-type stochastic dynamics. The lattice is formed by alternate layers of spins σ=5/2 and S=5/2. We employ the Glauber transition rates to construct the mean-field dynamic equations. First, we investigate the time variations of the average sublattice magnetizations to find the phases in the system and then the thermal behavior of the dynamic sublattice magnetizations to characterize the nature (first- or second-order) of the phase transitions and to obtain the dynamic phase transition (DPT) points. We also study the thermal behavior of the dynamic total magnetization to find the dynamic compensation temperature and to determine the type of the dynamic compensation behavior. We present the dynamic phase diagrams, including the dynamic compensation temperatures, in nine different planes. The phase diagrams contain seven different fundamental phases, thirteen different mixed phases, in which the binary and ternary combination of fundamental phases and the compensation temperature or the L-type behavior strongly depend on the interaction parameters.     

Nonequilibrium wetting transition in a nonthermal 2D Ising model

Nonequilibrium wetting transitions are observed in Monte Carlo simulations of a kinetic spin system in the absence of a detailed balance condition with respect to an energy functional. A nonthermal model is proposed starting from a two-dimensional Ising spin lattice at zero temperature with two boundaries subject to opposing surface fields. Local spin excitations are only allowed by absorbing an energy quantum (photon) below a cutoff energy E _c . Local spin relaxation takes place by emitting a photon which leaves the lattice. Using Monte Carlo simulation nonequilibrium critical wetting transitions are observed as well as nonequilibrium first-order wetting phenomena, respectively in the absence or presence of absorbing states of the spin system. The transitions are identified from the behavior of the probability distribution of a suitably chosen order parameter that was proven useful for studying wetting in the (thermal) Ising model.     

Phase transition features of the bond-dilution transverse ferromagnetic Ising spin system with random crystal field

The bond dilution spin-1 transverse ferromagnetic Ising model with random crystal field is investigated in the framework of effective field theory (EFT). The general expressions of magnetization are derived for lattice with any coordination number z. In particular, we calculate the phase diagrams of a square lattice. The second-order phase transition lines and the tricritical points are presented in different conditions for the square lattice. Special emphasis is placed on the influence of bond dilution, random crystal field and the transverse field on the phase diagrams. We discover some unusual phenomena. New results obtained in this paper are discussed in detail.