Dynamic phase transition and dynamic phase diagrams in the spin-5/2 Blume–Capel model under a time-dependent oscillating external field

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 (f_5/2), the ferromagnetic-1/2 (f_1/2) 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.     

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.     

Dynamic phase transitions and dynamic phase diagrams of the Blume–Emery–Griffiths model in an oscillating field: the effective-field theory based on the Glauber-type stochastic dynamics

Using the effective-field theory based on the Glauber-type stochastic dynamics (DEFT), we investigate dynamic phase transitions and dynamic phase diagrams of the Blume–Emery–Griffiths model under an oscillating magnetic field. We presented the dynamic phase diagrams in (T/J, h₀/J), (D/J, T/J) and (K/J, T/J) planes, where T, h₀, D, K and z are the temperature, magnetic field amplitude, crystal–field interaction, biquadratic interaction and the coordination number. The dynamic phase diagrams exhibit several ordered phases, coexistence phase regions and special critical points, as well as re-entrant behavior depending on interaction parameters. We also compare and discuss the results with the results of the same system within the mean-field theory based on the Glauber-type stochastic dynamics and find that some of the dynamic first-order phase lines and special dynamic critical points disappeared in the DEFT calculation.     

Dynamic phase transitions and dynamic phase diagrams in the kinetic spin-5/2 Blume-Capel model in an oscillating external magnetic field: Effective-field theory and the Glauber-type stochastic dynamics approach

Using an effective field theory with correlations, we study a kinetic spin-5/2 Blume-Capel model with bilinear exchange interaction and single-ion crystal field on a square lattice. The effective-field dynamic equation is derived by employing the Glauber transition rates. First, the phases in the kinetic system are obtained by solving this dynamic equation. Then, the thermal behavior of the dynamic magnetization, the hysteresis loop area and correlation are investigated in order to characterize the nature of the dynamic transitions and to obtain dynamic phase transition temperatures. Finally, we present the phase diagrams in two planes, namely (T/zJ, h₀/zJ) and (T/zJ, D/zJ), where T absolute temperature, h₀, the amplitude of the oscillating field, D, crystal field interaction or single-ion anisotropy constant and z denotes the nearest-neighbor sites of the central site. The phase diagrams exhibit four fundamental phases and ten mixed phases which are composed of binary, ternary and tetrad combination of fundamental phases, depending on the crystal field interaction parameter. Moreover, the phase diagrams contain a dynamic tricritical point (T), a double critical end point (B), a multicritical point (A) and zero-temperature critical point (Z).     

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.     

Dynamic phase transitions and dynamic phase diagrams of the spin-2 Blume-Capel model under an oscillating magnetic field within the effective-field theory

The dynamic phase transitions are studied in the kinetic spin-2 Blume-Capel model under a time-dependent oscillating magnetic field using the effective-field theory with correlations. The effective-field dynamic equation for the average magnetization is derived by employing the Glauber transition rates and the phases in the system are obtained by solving this dynamic equation. The nature (first- or second-order) of the dynamic phase transition is characterized by investigating the thermal behavior of the dynamic magnetization and the dynamic phase transition temperatures are obtained. The dynamic phase diagrams are constructed in the reduced temperature and magnetic field amplitude plane and are of seven fundamental types. Phase diagrams contain the paramagnetic (P), ferromagnetic-2 (F₂) and three coexistence or mixed phase regions, namely the F₂+P, F₁+P and F₂+F₁+P, which strongly depend on the crystal-field interaction (D) parameter. The system also exhibits the dynamic tricritical behavior.     

Dynamic magnetic hysteresis behavior and dynamic phase transition in the spin-1 Blume-Capel model

The nature (time variation) of response magnetization m(wt) of the spin-1 Blume-Capel model in the presence of a periodically varying external magnetic field h(wt) is studied by employing the effective-field theory (EFT) with correlations as well as the Glauber-type stochastic dynamics. We determine the time variations of m(wt) and h(wt) for various temperatures, and investigate the dynamic magnetic hysteresis behavior. We also investigate the temperature dependence of the dynamic magnetization, hysteresis loop area and correlation near the transition point in order to characterize the nature (first- or second-order) of the dynamic transitions as well as obtain the dynamic phase transition temperatures. The hysteresis loops are obtained for different reduced temperatures and we find that the areas of the loops are decreasing with the increasing of the reduced temperatures. We also present the dynamic phase diagrams and compare the results of the EFT with the results of the dynamic mean-field approximation. The phase diagrams exhibit many dynamic critical points, such as tricritical (•), zero-temperature critical (Z), triple (TP) and multicritical (A) points. According to values of Hamiltonian parameters, besides the paramagnetic (P), ferromagnetic (F) fundamental phases, one coexistence or mixed phase region, (F+P) and the reentrant behavior exist in the system. The results are in good agreement with some experimental and theoretical results.     

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.     

Effective-field theory with the differential operator technique for a kinetic Blume–Capel model with random diluted single-ion anisotropy

We present the dynamical phase diagrams of the kinetic Blume–Capel model with random diluted single-ion anisotropy in a square lattice under the presence of a time-varying (oscillating) external magnetic field calculated by an analytical method, the effective-field theory (EFT). The kinetics is modeled with the formalism of a master equation. The time-averaged magnetization (M$M$) acts as the order parameter and divides the temperature–field plane into three regions: ferromagnetic, paramagnetic, and coexistence of ferromagnetic and paramagnetic phases. In addition, the hysteresis loop area and the dynamic correlation function are calculated. It is observed that the inclusion of spin–spin correlations suppress the first-order transition lines and dynamical tricritical points for all values of the crystal-field concentration.     

Dynamic compensation temperature in the mixed spin-1 and spin-2 Ising model in an oscillating field on alternate layers of a hexagonal lattice

The dynamic behavior of a mixed spin-1 and spin-2 Ising system with a crystal-field interaction in the presence of a time-dependent oscillating external magnetic field on a hexagonal lattice is studied by using the Glauber-type stochastic dynamics. The lattice is formed by alternate layers of spins σ=1$\sigma =1$ and S=2. The Hamiltonian model includes intersublattice, intrasublattice and crystal-field interactions. The set of mean-field dynamic equations is obtained by employing the Glauber transition rates. Firstly, we study time variations of the average sublattice magnetizations in order to find the phases in the system, and the thermal behavior of the average sublattice magnetizations in a period or the dynamic sublattice magnetizations to obtain the dynamic phase transition points as well as to characterize the nature (continuous and discontinuous) of transitions. Then, the behavior of the dynamic total magnetization as a function of the temperature is investigated to find the dynamic compensation points as well as determine the type of behavior. We also present the dynamic phase diagrams for both presence and absence of the dynamic compensation temperatures in the nine different planes. According to the values of Hamiltonian parameters, besides the paramagnetic (p), antiferromagnetic (af), ferrimagnetic (i) and non-magnetic (nm) fundamental phases, eight different mixed phases and the compensation temperature or L- and N-types behavior in the Néel classification nomenclature exist in the system.     

Dynamic phase transition in the kinetic Blume--Emery--Griffiths model: Phase diagrams in the temperature and interaction parameters planes

As a continuation of our previously published work, the dynamic phase transitions are studied further, within a mean-field approach, in the kinetic Blume--Emery--Griffiths model in the presence of a time varying (sinusoidal) magnetic field by using the Glauber-type stochastic dynamics. The dynamic phase transitions are obtained and the phase diagrams are constructed in two different planes, namely in the reduced temperature (T) and biquadratic interaction (k) plane and found eight fundamental types of phase diagrams for various values of reduced crystal-field interaction (d) and magnetic field amplitude (h), and in the (T,?d) plane and obtained six distinct topologies for different values of k and h. Phase diagrams exhibit one or two dynamic tricritical points and a dynamic double critical end point, dynamic triple and quadruple points, and besides disordered and ordered phases, three coexistence phase regions exist in which occurring of these strongly depend on the values of d, k and h.     

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 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 phase transitions in the kinetic spin-1 Blume-Capel model on the Bethe lattice

The stationary states of the kinetic spin-1 Blume-Capel (BC) model on the Bethe lattice are analyzed in detail in terms of recursion relations. The model is described using a Glauber-type stochastic dynamics in the presence of a time-dependent oscillating external magnetic field (h) and crystal field (D) interactions. The dynamic order parameter, the hysteresis loop area and the dynamic correlation are calculated. It is found that the magnetization oscillates around nonzero values at low temperatures (T) for the ferromagnetic (F) phase while it only oscillates around zero values at high temperatures for the paramagnetic (P) phase. There are regions of the phase space where the two solutions coexist. The dynamic phase diagrams are obtained on the (kT/J,h/J) and (kT/J,D/J) planes for the coordination number q=4. In addition to second-order and first-order phase transitions, dynamical tricritical points and triple points are also observed.     

Magnetic field and temperature-induced first-order transition in Gd5(Si1.5Ge2.5): a study of the electrical resistance behavior

Magnetic field (0–4 T) and temperature dependencies (4.2–320 K) of the electrical resistance of Gd₅(Si_1.5Ge_2.5), which undergoes a reversible first-order ferromagnetic↔paramagnetic phase transition, have been measured. The electrical resistance of Gd₅(Si_1.5Ge_2.5) indicates that the magnetic phase transition can be induced by both temperature and magnetic field. The temperature dependence of the electrical resistance, R(T), for heating at low temperatures in the zero magnetic field has the usual metallic character, but at a critical temperature of T_cr=216 K the resistance shows a 20% negative discontinuity due to the transition from the low-temperature high-resistance state to the high-temperature low-resistance state. The R(T) dependence for cooling shows a similar but positive 25% discontinuity at 198 K. The isothermal magnetic field dependence of the electrical resistance from 212T224 K indicates the presence of temperature-dependent critical magnetic fields which can reversibly transform the paramagnetic phase into the ferromagnetic phase and vice versa. The critical magnetic fields diagram determined from the isothermal magnetic field dependencies of the electrical resistance of Gd₅(Si_1.5Ge_2.5) shows that the FM↔PM transition in zero magnetic field on cooling and heating occurs at 206 and 213 K, respectively. The full isothermal magnetic filed hysteresis for the FM↔PM transition is 2 T, and the isofield temperature gap between critical magnetic fields is 7 K.     

Monte Carlo study of dynamic phase transition in Ising metamagnet driven by oscillating magnetic field

The dynamical responses of Ising metamagnet (layered antiferromagnet) in the presence of a sinusoidally oscillating magnetic field are studied by Monte Carlo simulation. The time average staggered magnetisation plays the role of dynamic order parameter. A dynamical phase transition was observed and a phase diagram was plotted in the plane formed by field amplitude and temperature. The dynamical phase boundary is observed to shrink inward as the relative antiferromagnetic strength decreases. The results are compared with that obtained from pure ferromagnetic system. The shape of dynamic phase boundary observed to be qualitatively similar to that obtained from previous meanfield calculations.     

Influences of Crystal-Field and Interlayer Coupling Interactions on Dynamic Phase Diagrams of a Mixed-Spin(3/2,2) Bilayer System

Influences of crystal-fields(D_A and D_B) and interlayer coupling interactions(J_3) on dynamic magnetic critical behaviors of a mixed-spin(3/2, 2) bilayer system under an oscillating magnetic field are investigated by the Glauber-type stochastic dynamics based on the mean-field theory. For this purpose, dynamic phase diagrams are constructed in the reduced temperature and magnetic field amplitude plane for the ferromagnetic/ferromagnetic(FM/FM),antiferromagnetic/ferromagnetic(AFM/FM) and AFM/AFM interactions in detail. We observe that the influences of D_A, D_B and J_3 interactions parameters on the behavior of the dynamic phase diagrams are very much.     

Stochastic resonance and nonequilibrium dynamic phase transition of Ising spin system driven by a joint external field

The dynamic response and stochastic resonance of a kinetic Ising spin system （ISS） subject to the joint action of an external field of weak sinusoidal modulation and stochastic white-nolse are studied by solving the mean-field equation of motion based on Glauber dynamics. The periodically driven stochastic ISS shows that the characteristic stochastic resonance as well as nonequilibrium dynamic phase transition （NDPT） occurs when the frequency ω and amplitude h0 of driving field, the temperature t of the system and noise intensity D are all specifically in accordance with each other in quantity. There exist in the system two typical dynamic phases, referred to as dynamic disordered paramagnetic and ordered ferromagnetic phases respectively, corresponding to a zero- and a unit-dynamic order parameter. The NDPT boundary surface of the system which separates the dynamic paramagnetic phase from the dynamic ferromagnetic phase in the 3D parameter space of ho-t-D is also investigated. An interesting dynamical ferromagnetic phase with an intermediate order parameter of 0.66 is revealed for the first time in the ISS subject to the perturbation of a joint determinant and stochastic field. The intermediate order dynamical ferromagnetic phase is dynamically metastable in nature and owns a peculiar characteristic in its stability as well as the response to external driving field as compared with a fully order dynamic ferromagnetic phase.     

Glassy phase and thermodynamics for random field Ising model on spherical lattice in magnetic field

Phase diagram and thermodynamic parameters of the random field Ising model (RFIM) on spherical lattice are studied by using mean field theory. This lattice is placed in an external magnetic field (B). The random field (hi) is assumed to be Gaussian distributed with zero mean and a variance     

Dynamic hysteresis behaviors in the kinetic Ising system on triangular lattice

We studied dynamic hysteresis behaviors of the spin-1 Blume-Capel (BC) model in a triangular lattice by means of the effective-field theory (EFT) with correlations and using Glauber-type stochastic dynamics. The effects of the exchange interaction (J), crystal field (D), temperature (T) and oscillating frequency (w) on the hysteresis behaviors of the BC model in a triangular lattice are investigated in detail. Results are compared with some other dynamic studies and quantitatively good agreement is found.