The mixed-spins 1/2 and 3/2 Blume—Capel model with a random crystal field

The random crystal field(RCF) effects are investigated on the phase diagrams of the mixed-spins 1/2 and 3/2 Blume-Capel(BC) model on the Bethe lattice.The bimodal random crystal field is assumed and the recursion relations are employed for the solution of the model.The system gives only the second-order phase transitions for all values of the crystal fields in the non-random bimodal distribution for given probability.The randomness does not change the order of the phase transitions for higher crystal field values,i.e.,it is always second-order,but it may introduce first-order phase transitions at lower negative crystal field values for the probability in the range about 0.20 and 0.45,which is only the second-order for the non-random case in this range.Thus our work claims that randomness may be used to induce first-order phase transitions at lower negative crystal field values at lower probabilities.     

The spin-1 Blume-Capel model with random crystal field on the Bethe lattice

The dependence of the phase diagrams on the random crystal field (RCF) is investigated for the spin-1 Blume-Capel (BC) model on the Bethe lattice. The calculations are carried out in terms of the recursion relations for the coordination number z=4 which corresponds to the square lattice. The model presents tricritical points which are observed at lower negative crystal fields and higher temperatures for higher probabilities p and which vanish at lower p’s. The effect of randomness is illustrated for p=0.5 and shown that it changes the phase diagrams drastically from random to non-random systems. The reentrant behavior is also observed for appropriate p values.     

Effects of the randomly distributed magnetic field on the phase diagrams of the Ising Nanowire II: Continuous distributions

The effect of the random magnetic field distribution on the phase diagrams and ground state magnetizations of the Ising nanowire has been investigated with effective field theory with correlations. Gaussian distribution has been chosen as a random magnetic field distribution. The variation of the phase diagrams with that distribution parameters has been obtained and some interesting results have been found such as disappearance of the reentrant behavior and first order transitions which appear in the case of discrete distributions. Also for single and double Gaussian distributions, ground state magnetizations for different distribution parameters have been determined which can be regarded as separate partially ordered phases of the system.     

Reentrant behavior of magnetic ordered phase in spin-crossover solids with quenched disordered ligand field

The Ising-like model of spin-crossover solid compounds with quenched random ligand field has been investigated by the mean-field (infinite-range) approximation. An exact solution for the problem is found within the replica formalism. The magnetic diagrams are obtained; the relations between the intermolecular coupling and the temperature as well as the reentrant phenomena of the magnetic ordered phase are discussed.     

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.     

Effects of the randomly distributed magnetic field on the phase diagrams of Ising nanowire I: Discrete distributions

The effect of the random magnetic field distribution on the phase diagrams and ground state magnetizations of Ising nanowire is investigated using effective field theory with correlations. Trimodal distribution has been chosen as a random magnetic field distribution. The variation of the phase diagrams with that distribution parameters has been obtained and some interesting results have been found such as reentrant behavior and first order transitions. Also for the trimodal distribution, ground state magnetizations for different distribution parameters have been determined which can be regarded as separate partially ordered phases of the system.     

Thermodynamical Properties of Spin-3/2 Ising Model in a Longitudinal Random Field with Crystal Field

A theoretical study of a spin-3/2 Ising model in a longitudinal random field with crystal field is studied by using of the effective-field theory with correlations. The phase diagrams and the behavior of the tricritical point are investigated numerically for the honeycomb lattice when the random field is bimodal. In particular, the specific heat and the internal energy are examined in detail for the system with a crystal-field constant in the critical region where the ground-state configuration may change from the spin-3/2 state to the spin-1/2 state. We find many interesting phenomena in the system.     

Phase transition properties of ferroelectric thin films with two surface layers

The phase diagrams of ferroelectric thin films with two surface layers described by the transverse Ising model have been studied under the mean-field approximation. We discuss the effects of the exchange interaction and transverse field parameters on the phase diagrams. The results indicate that the phase transition properties of the phase diagrams can be greatly modified by changing the transverse Ising model parameters. In addition, the crossover features of the parameters from the ferroelectric dominant phase diagram to the paraelectric dominant phase diagram are determined for ferroelectric thin films with two surface layers.     

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.     

Thermodynamical Properties of Spin-3/2 Ising Model in a Longitudinal Random Field with Crystal Field

A theoretical study of a spin-3/2 Ising model in a longitudinal random field with crystal field is studiedby using of the effective-field theory with correlations. The phase diagrams and the behavior of the tricritical point areinvestigated numerically for the honeycomb lattice when the randorm field is bimodal. In particular, the specific heatand the internal energy are examined in detail for the system with a crystal-field constant in the critical region wherethe ground-state configuration may change from the spin-3/2 state to the spin-1/2 state. We find many interestingphenomena in the system.     

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.     

Longitudinal-Random-Field Mixed Ising Model with Arbitrary Spins

The longitudinal-random-fieM mixed Ising model consisting of arbitrary spin values has been studied by the use of an effective field theory with correlations （EFT）. The phase diagrams of systems with mixed spins： σ = 1/2, S = 1; σ = 1/2, S = 3/2 are plotted. Not only the discontinuity at T = 0 K, is found when both longitudinal fields are trimodal distributed, but also the trieritical behavior is observed in these phase diagrams between the bimodal and trimodal distributions of longitudinal fields, which is different from the single-spin one. The appearance of tricritical point is independent of the coordination number and spin values.     

Random field effects on the anisotropic quantum Heisenberg model with Gaussian random magnetic field distribution

The effect of a zero-centered Gaussian random magnetic field distribution on the phase transition properties of the anisotropic quantum Heisenberg model has been investigated on a honeycomb lattice within the framework of effective field theory (EFT) for a two-spin cluster (which is abbreviated as EFT-2). Particular attention has been devoted to investigation of the effect of the anisotropy in the exchange interaction on a system with Gaussian random magnetic field distribution. The variation of the critical temperature with the randomness parameter (i.e., the width of the distribution) has been obtained for several anisotropy parameters. Critical Gaussian distribution width values, which make the critical temperature zero, have been obtained. Moreover, it has been concluded that all critical temperatures are of second order, and that reentrant behavior does not exist in the phase diagrams.     

Random field effects on the phase diagrams of spin-1/2 Ising model on a honeycomb lattice

The Ising model with quenched random magnetic fields is examined for single Gaussian, bimodal and double Gaussian random field distributions by introducing an effective field approximation that takes into account the correlations between different spins that emerge when expanding the identities. Random field distribution shape dependence of the phase diagrams, magnetization and internal energy is investigated for a honeycomb lattice with a coordination number q=3. The conditions for the occurrence of reentrant behavior and tricritical points on the system are also discussed in detail.     

Phase Diagram and Tricritical Behavior of a Spin-2 Transverse Ising Model in a Random Field

The phase diagrams of a spin-2 transverse Ising model with a random field on honeycomb, square, and simple-cubic lattices, respectively, are investigated within the framework of an effective-field theory with correlations.We find the behavior of the tricritical point and the reentrant phenomenon for the system with any coordination number z, when the applied random field is bimodal. The behavior of the tricritical point is also examined as a function of applied transverse field. The reentrant phenomenon comes from the competition between the transverse field and the random field.     

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).     

双模随机晶场对纳米管上Blume-Capel模型磁化强度和相变的影响

近年来, 磁性纳米管的物理性质和相关应用得到了人们的广泛关注. 利用有效场理论研究了纳米管上双模随机晶场中Blume-Capel模型的磁化强度和相变性质, 得到了系统的磁化强度与温度和随机晶场的关系及其相图. 结果表明: 系统在稀释晶场、交错晶场和同向晶场中会表现出不同的磁学性质和相变行为; 稀释晶场和交错晶场会抑制系统的磁化强度, 导致其基态饱和值小于1, 而同向晶场则不会; 随着随机晶场参量的变化, 系统存在多个相变温度, 并呈现出三临界现象和重入现象.     

Phase diagrams of spin-1 Ising model with bilinear and quadrupolar interactions under magnetic field. Two-particle cluster approximation

The spin-1 Ising model with bilinear and quadrupolar short-range interactions under magnetic field is investigated within the two-particle cluster approximation. It is shown that for those values of the quadrupolar interaction when at zero magnetic field the system undergoes a temperature phase transition between quadrupolar and paramagnetic phases, a triple point may exist in the temperature vs. magnetic field phase diagrams, necessarily along with a critical point. It is also shown that the critical points in the temperature vs. magnetic field phase diagrams of the investigated model can be of three types.     

Critical behaviours and magnetic properties of three-dimensional bond and anisotropy dilution Blume——Capel model in the presence of an applied field

This paper studies the critical behaviours and magnetic properties of three-dimensional bond and anisotropy dilution Blume--Capel model (BCM) in the presence of an applied field within the effective field theory. The trajectory of tricritical point, reentrant transitions and degenerate patterns of anisotropy are obtained both for the bond and the anisotropy dilutions. The global phase diagrams demonstrate unusually reentrant phenomena. The temperature dependences of magnetization curves undergo remarkable spin glass behaviour at low temperatures, and transform from ferromagnetism to paramagnetism at high temperature in applied fields. Temperature dependence of magnetic susceptibility curve is in qualitative agreement with experimental result.     

The temperature-dependent phase diagrams of the spin-3/2 Ising model on a FM/AFM two-layer lattice with a crystal field

The temperature-dependent phase diagrams of the spin-3/2 Ising model on a two-layer Bethe lattice with ferromagnetic (FM)/antiferromagnetic (AFM) intra-layer and either FM or AFM type inter-layer interactions are investigated under a constant magnetic field (H) and in the presence of a crystal field (D) by using exact recursion equations in a pairwise approach for coordination numbers q=3,4 and 6, in detail. In the light of the ground-state (GS) phase diagrams, the temperature-dependent phase diagrams of the model are obtained by studying the thermal variations of the order parameters, response functions and free energy. Then, they are illustrated on the (kT/J₁,J₃/J₁) and (kT/J₁,J₂/J₁) planes for the given system parameters. It is observed that the system exhibits first- and second-order phase transitions for all q values, and hence, in some cases, tricritical points. The existence of critical-end points and that of isolated points are also observed. The re-entrant behavior owes its presence to the two Néel temperatures, T_N, that are present for all q.