Phase diagrams in mixed spin-3/2 and spin-2 Ising system with two alternative layers within the effective-field theory

The phase diagrams in the mixed spin-3/2 and spin-2 Ising system with two alternative layers on a honeycomb lattice are investigated and discussed by the use of the effective-field theory with correlations. The interaction of the nearest-neighbour spins of each layer is taken to be positive (ferromagnetic interaction) and the interaction of the adjacent spins of the nearest-neighbour layers is considered to be either positive or negative (ferromagnetic or anti-ferromagnetic interaction). The temperature dependence of the layer magnetizations of the system is examined to characterize the nature (continuous or discontinuous) of the phase transitions and obtain the phase transition temperatures. The system exhibits both second-and first-order phase transitions besides triple point (T P ), critical end point (E), multicritical point (A), isolated critical point (C) and reentrant behaviour depending on the interaction parameters. We have also studied the temperature dependence of the total magnetization to find the compensation points, as well as to determine the type of behaviour, and N-type behaviour in N′eel classification nomenclature existing in the system. The phase diagrams are constructed in eight different planes and it is found that the system also presents the compensation phenomena depending on the sign of the bilinear exchange interactions.     

Hexagonal Type Ising Nanowire with Spin-1 Core and Spin-2 Shell Structure

Thermodynamic properties and phase diagrams of a mixed spin-(1,2) Ising ferrimagnetic system with single ion anisotropy on hexagonal nanowire are studied by using effective-field theory with correlations. The susceptibility, internal energy and specific heat of the system are numerically examined and some interesting phenomena in these quantities are found. The effect of the Hamiltonian parameters on phase diagrams are examined in detail. Besides second-order phase transition, lines of first-order transition and tricritical points are found. In particular, we found that for some negative values of single-ion anisotropies, there exist first-order phase transitions.     

Cylindrical Ising nanowire with crystal field: existence of a dynamic compensation temperatures

We present a study, within a mean-field theory, of the kinetics of the spin-1 Blume–Capel model on cylindrical Ising nanowire 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 thermal behavior of the dynamic order parameters. From these studies, we obtain the dynamic phase transition (DPT) points. Then, we study the temperature dependence of the dynamic total magnetization to find the dynamic compensation points as well as to determine the type of behavior. We also investigate the effect of interaction parameters on the compensation phenomenon and construct the phase diagrams in four different planes. The system exhibits the compensation temperatures, or the N-, P-, Q-, S-type behaviors. Furthermore, we also observed two-compensation temperatures, namely W-type behaviors, whose result is compared with some experimental works and a good overall agreement is found.     

The dynamic phase transition in the spin-1/2 Ising system within the path probability method

We study the dynamic phase transitions and present the dynamic phase diagrams of the spin-1/2 Ising system under the presence of a time-varying (sinusoidal) external magnetic field within the path probability method (PPM) of Kikuchi and we observe that the PPM gives exactly the same result as with the Glauber-type stochastic dynamics based on the mean-field theory (DMFT). We also investigate the influence of the rate constant on the dynamic phase diagrams in detail and five new and interesting dynamic phase diagrams are found. We notice that the derivation of the dynamic equations by using the PPM is more clear and easier than within the DMFT and the Glauber-type stochastic dynamics based on the effective-field theory (DEFT). The advantages and disadvantages of the PPM over the DMFT and DEFT are also discussed.     

Dynamic magnetic properties in the kinetic mixed spin-2 and spin-5/2 Ising model under a time-dependent magnetic field

We extend the recent paper [W. Jiang, V-C. Lo, B-D. Bai, J. Yang, Physica A 389 (2010) 2227-2233] to present a study, within a mean-field approach, the dynamic magnetic properties of the mixed spin-2 and spin-5/2 Ising ferrimagnetic system, which corresponds the molecular-based magnetic materials AFe^IIFe^III(C₂O₄)₃ [ A=N(n-C_nH_2n+1)₄, n=3-5], by using the Glauber-type stochastic dynamics. This mixed Ising ferrimagnetic system is used on a layered honeycomb lattice in which Fe^II (S=5/2) and Fe^III (σ=2) occupy sites. First, we investigate the time variations of average order parameters to find the phases in the system and then the thermal behavior of the dynamic order parameters to obtain the dynamic phase transition (DPT) points as well as to characterize the nature (first-or second-order) phase transitions. We also present the dynamic phase diagrams and study the dynamic magnetic hysteresis loop behaviors of the kinetic mixed spin-2 and spin-5/2 Ising ferrimagnetic system. The results are compared with some experimental and theoretical works and a good overall agreement is found.     

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.     

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 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).     

Dynamic phase transitions and the effects of frequency of oscillating magnetic field on the dynamic phase diagrams in the bilayer honeycomb lattice with AB stacking geometry

We study some dynamic properties of the bilayer honeycomb lattice with AB stacking geometry in the presence of a time-dependent oscillating external magnetic field. We employ the Glauber transition rates to construct the mean-field dynamical equations. First, we obtain dynamic phases in the system and observe the paramagnetic (p), ferromagnetic (f), compensated (c) antiferromagnetic (af), surface ferromagnetic (sf) and mixed (m) phases. Besides, coexistence phase regions also exist in the system. Second, we investigate the thermal behavior of the dynamic order parameters. From these study, the natures (first- or second-order) of the transitions are characterized and the dynamic phase transition (DPT) points are presented. The DPTs are obtained and the dynamic phase diagrams (DPD) are constructed plane of the temperature versus the amplitude of the magnetic field. We investigate the effect of the frequency of the oscillating external magnetic field on the DPD.     

Dynamic compensation temperatures in a mixed spin-1 and spin-3/2 Ising system under a time-dependent oscillating magnetic field

We study the existence of dynamic compensation temperatures in the mixed spin-1 and spin-3/2 Ising ferrimagnetic system Hamiltonian with bilinear and crystal-field interactions in the presence of a time-dependent oscillating external magnetic field on a hexagonal lattice. We employ the Glauber transitions rates to construct the mean-field dynamic equations. We investigate the time dependence of an average sublattice magnetizations, the thermal behavior of the dynamic sublattice magnetizations and the total magnetization. From these studies, we find the phases in the system, and characterize the nature (continuous or discontinuous) of transitions as well as obtain the dynamic phase transition (DPT) points and the dynamic compensation temperatures. We also present dynamic phase diagrams, including the compensation temperatures, in the five different planes. A comparison is made with the results of the available mixed spin Ising systems.     

Spin-1/2 Ising model on a AFM/FM two-layer Bethe lattice in a staggered magnetic field

A bilayer spin-1/2 Ising model consisting of two superposed Bethe lattices with antiferromagnetic/ferromagnetic interactions is studied by the use of exact recursion relations in a pairwise approach in the presence of an external staggered magnetic field. Besides the ground state phase diagrams calculated in different possible planes of the model parameters space, the thermal variations of the order-parameters and the free energy are investigated to obtain the temperature-dependent phase diagrams of the model for different values of the coordination numbers q. Our calculations reveal that depending on the strength of the model parameters, the model exhibits a variety of interesting phase transitions and therefore phase diagrams.     

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 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.