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.     

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.     

The effective-field theory studies of critical phenomena in a mixed spin-1 and spin-2 Ising model on honeycomb and square lattices

An effective-field theory with correlations has been used to study critical behaviors of a mixed spin-1 and spin-2 Ising system on a honeycomb and square lattices in the absence and presence of a longitudinal magnetic field. The ground-state phase diagram of the model is obtained in the longitudinal magnetic field (h) and a single-ion potential or crystal-field interaction (Δ) plane. The thermal behavior of the sublattice magnetizations of the system are investigated to characterize the nature of (continuous and discontinuous) of the phase transitions and obtain the phase transition temperature. The phase diagrams are presented in the (Δ/|J|, k_BT/|J|) plane. The susceptibility, internal energy and specific heat of the system are numerically examined and some interesting phenomena in these quantities are found due to the absence and presence of the applied longitudinal magnetic field. Moreover, the system undergoes second- and first-order phase transition; hence, the system gives a tricritical point. The system also exhibits reentrant behavior.     

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.     

Magnetic properties of mixed Ising system with random field

A spin-1/2 and spin-3/2 mixed Ising system in a random field is studied by the use of effective-field theory with correlations. The phase diagrams and thermal behaviours of magnetizations are investigated numerically for the honeycomb lattice (z=3) and square lattice (z=4) respectively. The tricritical behaviours for both honeycomb and square lattices, as well as the reentrant behaviour for the square lattice are found.     

Nanoparticle with a ferrimagnetic interlayer coupling in the presence of single-ion anisotropis

The magnetic properties of a nanoparticle described by the transverse Ising model with single-ion anisotropis, which consists of a concentric spin-3/2 core and a hexagonal ring spin-5/2 shell coupled with a ferrimamagnetic interlayer coupling, are studied by the effective-field theory with self-spin correlations. Particular emphasis is given to the effects of the both the transverse field and the single-ion anisotropis on the longitudinal and transverse magnetizations, phase diagrams of the nanoparticle. We have found that, for appropriate values of the system parameters, one or two compensation points may be obtained in the present systems.     

Phase diagrams of the spin-2 Ising model in the presence of a quenched diluted crystal field distribution

We have investigated the random crystal field effects on the phase diagrams of the spin-2 Blume-Capel model for a honeycomb lattice using the effective-field theory with correlations.To do so,the thermal variations of magnetization are studied via calculating the phase diagrams of the model.We have found that the model displays both second-order and first-order phase transitions in addition to the tricritical and isolated points.Reentrant behavior is also observed for some appropriate values of certain system parameters.Besides the usual ground-state phases of the spin-2 model including ±2,±1,and 0,we have also observed the phases ±3/2 and ±1/2,which are unusual for the spin-2 case.     

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.     

Ferrimagnetism and reentrant phenomena in a tetragonal Ising nanoparticle

ABSTRACT

The phase diagrams and magnetizations in a tetragonal Ising nanoparticle have been investigated by using the effective-field theory with correlations and the core–shell model. For the spin-1/2 atoms in the shell, a transverse field is included to cant their spin direction. The results show that they are heavily dependent on the given physical parameters. The ferrimagnetic behaviours, as well as novel type behaviours, have been found in the thermal variation of magnetization. The reentrant phenomena are also obtained.     

Phase diagrams of a nonequilibrium mixed spin-1/2 and spin-2 Ising ferrimagnetic system under a time-dependent oscillating magnetic field

We present phase diagrams for a nonequilibrium mixed spin-1/2 and spin-2 Ising ferrimagnetic system on a square lattice in the presence of a time dependent oscillating external magnetic field. We employ the Glauber transition rates to construct the mean-field dynamical 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 dynamic phase transition points are obtained and the phase diagrams are presented in two different planes. Phase diagrams contain paramagnetic (p) and ferrimagnetic (i) phases, and one coexistence or mixed phase region, namely the i+p, that strongly depend on interaction parameters. The system exhibits the dynamic tricritical point and the reentrant behaviors.     

Dynamic magnetic properties of the kinetic cylindrical Ising nanotube

The nature (time variation) of response magnetizations m(wt) of the kinetic cylindrical Ising nanotube 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 have determined the time variations of m(wt) and h(wt) for various temperatures, and investigated the dynamic magnetic hysteresis behavior. Temperature dependence of the dynamic magnetizations, hysteresis loop areas and correlations are investigated in order to characterize the nature (first- or second-order) of the dynamic transitions as well as to obtain the dynamic phase transition temperatures. We also present the dynamic phase diagrams in the three different planes and compare the results of the equilibrium and nonequilibrium states. The phase diagrams exhibit dynamic tricritical, isolated critical, multicritical and triple points. The results are in good agreement with some experimental and theoretical results.     

Properties of the ground state in a spin-2 transverse Ising model with the presence of a crystal field

The properties of the ground state in the spin-2 transverse Ising model with the presence of a crystal field are studied by using the effective-field theory with correlations. The longitudinal and transverse magnetizations, the phase diagram and the internal energy in the ground state are given numerically for a honeycomb lattice (z=3).     

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).     

An antiferromagnetic transverse Ising nanoisland; unconventional surface effects

The phase diagrams and temperature dependences of magnetizations in a transverse Ising nanosisland with an antiferromagnetic spin configuration are studied by the use of the effective-field theory with correlations (EFT). Some novel features, such as the re-entrant phenomena with two compensation points being free from disorder induced frustration, are obtained for the magnetic properties in the system.     

Ground-state magnetic properties of the spin-2 transverse Ising model

The ground-state magnetic properties of the spin-2 transverse Ising model with a longitudinal crystal field are studied within the framework of mean-field theory (MFT) and effective-field theory (EFT), respectively. The phase diagrams and magnetization curves are examined in detail. It is found that the system exhibits a tricritical behavior in the ground-state phase diagrams. Some interesting phenomena have been found, especially the first-order phase transition from one ordered phase to the other ordered phase, which is due to the high spin. The spin correlation has important effect on the magnetic properties of the system. We also find that the ground-state phase diagrams of the spin-2 transverse Ising model are very different from those of the spin-3/2 transverse Ising model.     

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.     

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.     

Magnetic properties of a mixed spin- 1/2 and spin- 3/2 transverse Ising model in a longitudinal magnetic field

The mixed spin- 1/2 and spin- 3/2 transverse Ising model in a longitudinal magnetic field is studied within the framework of the effective-field theory with correlations. In this approach the effective-field equations are derived by using a probability distribution method based on the generalized but approximated van der Waerden identities. The total longitudinal and transverse magnetizations, the transverse susceptibility and longitudinal susceptibility and the critical temperatures are obtained. We find a number of interesting phenomena in these quantities, due to the applied transverse field and the longitudinal field.     

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.     

Magnetic properties of a hexagonal transverse Ising nanoisland

The magnetic properties of a hexagonal transverse Ising nanoisland have been calculated by the effective-field theory with correlations. The effects of surface coupling, interlayer coupling, and the competition between transverse fields at the surface shell and in the inner core on phase diagrams and magnetizations are examined. Meanwhile, the results are also compared with two different nanoislands which consist of two layers with nine atoms or five atoms in each of the layers.