The phase diagrams of a spin-1 transverse Ising model

The phase diagrams of the spin-1 transverse Ising model with the presence of a crystal field is investigated by using an effective-field theory (EFT). We give a method to calculate the Gibbs free energy numerically at finite temperature within the EFT. The first-order transition lines are obtained by comparing the Gibbs free energy. The phase diagrams and the Gibbs free energy are also compared with those given using the mean-field theory (MFT).     

Phase transitions and multicritical points in the mixed spin-3/2 and spin-2 Ising model with different single-ion anisotropies

The phase diagram of mixed spin-3/2 and spin-2 Ising ferromagnetic model with different single-ion anisotropies is investigated by the use of a mean-field theory based on the Bogoliubov inequality for the Gibbs free energy. Global phase diagrams are obtained in the temperature-anisotropy plane. In particular, by changing values of the single-ion anisotropies, several different types of phase diagrams of first-order transition between two ordered phases, are studied in detail. A variety of multicritical points such as tricritical points, isolated critical points, and triple points are obtained.     

Effect of the transverse field on the site-diluted Ising model in a longitudinal random field

Phase diagrams and magnetization curves of a diluted spin-3/2 transverse Ising model in a random field on honeycomb lattices are investigated by the use of an effective-field theory with correlations. The tricritical point is found in the system, in contrast to the corresponding spin-1/2 Ising counterpart. The possible reentrant phenomena displayed by the system due to the competition effects that occur for appropriate ranges of the random and transverse fields are investigated.     

Ground-state phase diagrams of Ising metamagnet in a mixed longitudinal and transverse magnetic field

The ground-state magnetic properties of a two-sublattice Ising metamagnet in a mixed longitudinal and transverse magnetic field are studied within the effective-field theory. A parameter j₂=J₂/J₁ is introduced, which reflects the strength ratio of spin coupling between adjacent planes and in each plane. In addition to the second-order transition lines, the first-order transition lines are also presented, since the ground-state energy can be calculated numerically. The ground-state phase diagrams in h_x–h_z are presented. The results show that when j₂<0 the phase transition of the system is always first-order for h_x<2.751, and when −1000?j₂<0 it is always second-order for h_x>4.36. For the given h_x (0<h_x<14.71), the longitudinal critical magnetic field increases as j₂ decreases. The reentrant phenomenon occurs in the range of j₂<−11.89, h_x>14.71. There is no fourth-order critical point in the phase diagrams given by using EFT as found by using mean field theory (MFT).     

The possibility of two compensation points in a ferrimagnetic mixed spin-1 and spin-3/2 Ising system using Bethe lattice approach

We give an exact formulation of a mixed spin-1 and spin-3/2 Ising model on the Bethe lattice, which shows ferrimagnetism and compensation points. The model incorporates antiferromagnetic nearest-neighbor interaction which is relevant to describe ferrimagnetism. The influence of two sublattice crystal fields, D_A and D_B, on compensation points is studied in detail. For certain crystal-field values, the single or double compensation temperature may occur in the present system.     

Frequency dependence of the complex susceptibility for a spin-1 Ising model

The complex susceptibility or the dynamic susceptibility (χ(ω)=χ′(ω)−iχ″(ω)) for a spin-1 Ising system with bilinear and biquadratic interactions is obtained on the basis of Onsager theory of irreversible processes. If the logarithm of the susceptibilities is plotted as a function of the logarithm of frequency, then the real part (χ′) displays a sequence of plateau regions and the imaginary part (χ″) has a sequence of maxima in the ordered or ferromagnetic phase. On the other hand, only one plateau region in χ′ and one maximum in χ″ is observed in the disordered or paramagnetic phase. Argand or Cole-Cole plots (χ″−χ′) for a selection of temperatures are also shown, and a sequence of semicircles is illustrated in the ordered phase and only one semicircle for the disordered phase in these plots.     

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).     

Magnetic relaxation in a spin-1 Ising model near the second-order phase transition point

The magnetic relaxation of a spin-1 Ising model with bilinear and biquadratic interactions is formulated within the framework of statistical equilibrium theory and the thermodynamics of irreversible processes. Using a molecular-field expression for the magnetic Gibbs energy, the magnetic Gibbs energy produced in the irreversible process is calculated and time derivatives of the dipolar and quadrupolar order parameters are treated as fluxes conjugate to their appropriate generalized forces in the sense of Onsager theory. The kinetic equations are obtained by introducing kinetic coefficients that satisfy the Onsager relation. By solving these equations an expression is derived for the dynamic or complex magnetic susceptibility. From the real and imaginary parts of this expression, magnetic dispersion and absorption factor are calculated and analyzed near the second-order phase transition.     

Ground-state phases and quantum phase transitions in a two-dimensional spin-1/2 XY model with four-spin interactions

We discuss the ground state phase transition between an antiferromagnet and a valence-bond solid in a two-dimensional spin-1/2 XY model with a four-spin interaction. This transition has been proposed as a candidate for a deconfined quantum-critical point. We analyze quantum Monte Carlo data in order to accurately characterize the transition. The central question that remains to be answered is whether the transition really is continuous, or whether it is actually weakly first-order. We present the current status of both ground state and finite-temperature calculations. Based on the results, we discuss possible scenarios for the transition, none of which is consistent with deconfined quantum-criticality. However, we argue that a deconfined quantum-critical point may be located nearby in an extended parameter space.We also discuss the staggered Ising phase obtaining in the limit of strong four-spin coupling.     

Magnetic properties of Ising metamagnet in both external longitudinal and transverse fields

The phase diagrams of a two-sublattice Ising metamagnet at finite temperature in a mixed longitudinal field and a transverse magnetic field are investigated by the use of an effective-field theory (EFT) with correlations. In addition to the second-order transition lines, the first-order transition lines are also presented in the phase diagrams, since the Gibbs free energy can be calculated numerically. The results show that there is no fourth-order critical line in the phase diagrams given by using EFT as found by using mean-field theory (MFT). The tricritical lines and their projection in the t−h_x plane obtained by using EFT are also quite different from those by using MFT. Only one type of phase diagram is obtained by using EFT while three kinds of phase diagrams are obtained by using MFT, which indicates that only the first kind of phase diagrams obtained by using MFT is reliable. Furthermore, it is shown that the region of first-order transitions increases as the transverse magnetic field h_x decreases.     

Critical properties of the biaxial Ising model with both the longitudinal crystal field and the transverse dilution crystal field

Within the effective field theory (EFT), the critical properties of the biaxial Ising model with both longitudinal crystal field and transverse dilution crystal field are investigated for a simple cubic lattice. The tricritical point (TCP) and its trajectory are discussed in T-D_x and T-D_z space. A new phenomenon of two TCPs is found in T-D_x space. There exists a second-order line between two first-order lines, separated by two TCPs. The change of dilution concentration leads to a complex relation of the trajectory of the TCP. The degenerate patterns at the ground state appear by changing the longitudinal crystal field. The range of the ordered phase for transition lines labelled as a positive or (negative) value of D_x/J becomes larger or (smaller) with the decrease of t_x in T-D_z space. Some results have not been revealed in previous works.     

Effects of transverse field on the magnetization and initial susceptibility of a molecular-based magnet

The molecular-based magnet system consists of mixed spin-2 and spin- 5/2 honeycomb lattices with ferrimagnetic interlayer coupling. Within the framework the effective-field theory with self-spin correlations and differential operator technique, the effects of the transverse field on the magnetization and initial susceptibility have been studied in detail.     

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.     

Exact results of a mixed spin-1/2 and spin-1 Ising chain with both longitude and transverse single-ion anisotropies

The mixed spin-1/2 and spin-1 Ising chain with both longitude and transverse single-ion anisotropies Dz and Dx is solved exactly by means of a mapping to the spin-1/2 Ising chain with the alternating transverse fields and the Jordan-Wigner transformation. The analytical expressions of the quasi-particles' spectra Λk, the minimal energy gap Δ₀ for exciting a fermion quasi-particle, the minimal energy gap Δh for exciting a hole, and the ground state energy are obtained. The phase diagram of the ground state is also given. The results show that when Dz?0 for any finite value of Dx, there is no quantum critical point and the ground state is always in a spin ordered phase disregard of the boundary condition in the present system.     

Transitions involving conical magnetic phases in a model with bilinear and biquadratic interactions

In a previous work a model was proposed for the phase transitions of crystals with localized magnetic moments which at low temperature have a “conical” arrangement that at higher T transforms into a more symmetrical structure (depending on the compound) before becoming totally disordered. The model assumes bilinear and biquadratic interactions between magnetic moments up to the fifth neighbours, and for any given T the structure with the least free energy is obtained by a mean-field approximation (MFA). The interaction constants are derived from ab initio   energy calculations. In this work we improve upon that model modifying the MFA in such a way that a continuous (instead of discontinuous) spectrum of excited states is available to the system. In the previous work, which dealt with _LaMn2Ge2${\mathrm{LaMn}}_2{\mathrm{Ge}}_2$ and _LaMn2Si2${\mathrm{LaMn}}_2{\mathrm{Si}}_2$, we found that transitions to different structures can be obtained for increasing T, in good qualitative agreement with experiment. The critical temperatures, however, were exaggeratedly high. With the new MFA we obtain essentially the same behaviour concerning the phase transitions, and critical temperatures much closer to the experimental ones.     

Ground state phase diagrams and the tricritical behaviors of Ising metamagnet in both external longitudinal and transverse field

The ground state magnetic properties of a two-sublattice Ising metamegnet in both external longitudinal and transverse fields are studied within the mean-field approach. A parameter α=(Z₁J₁+Z₂J₂)/(Z₁J₁−Z₂J₂) which reflects the strength ratio of spin coupling in the plane and in adjacent planes is introduced. The ground state energy, the longitudinal staggered magnetization, the longitudinal total magnetization and the transverse total magnetization are calculated. The ground state phase diagrams in Ω−h and Ω−α plane are presented. The results show that when Ω is given, the longitudinal critical magnetic field increases when α decreases; the phase transition changes always from first order to second order with increase in the longitudinal magnetic field h or decrease in α. The reentrant phenomenon occurs in the range α?−0.66, Ω?0.21, h?0.78.     

A crystal field investigation of the properties of RCuAs2 (R=Pr, Nd, Sm, Tb, Dy, Ho, Er and Yb)

A crystal field (CF) investigation of the magnetic properties and heat capacities of RCuAs₂ (R=Pr, Nd, Sm, Tb, Dy, Ho, Er and Yb) has been carried out using the observed average magnetic susceptibilities (1.8-300 K) of the title compounds. The CF parameters proposed for the systems show a systematic variation throughout the rare-earth series. Other physical properties dependent on the CF are also computed and compared with available experimental data. The experimental heat capacity data reported for a limited range of temperature agree well with computed heat capacity for all the compounds (except SmCuAs₂ and YbCuAs₂). CF J mixing was found to be appreciable for all the samples except YbCuAs₂.     

Kinetics of a mixed spin-1/2 and spin-3/2 Ising ferrimagnetic model

We present a study, within a mean-field approach, of the kinetics of a mixed ferrimagnetic model on a square lattice in which two interpenetrating square sublattices have spins that can take two values, , alternated with spins that can take the four values, . We use the Glauber-type stochastic dynamics to describe the time evolution of the system with a crystal-field interaction in the presence of a time-dependent oscillating external magnetic field. The nature (continuous and discontinuous) of transition is characterized by studying the thermal behaviors of average order parameters in a period. The dynamic phase transition points are obtained and the phase diagrams are presented in the reduced magnetic field amplitude (h) and reduced temperature (T) plane, and in the reduced temperature and interaction parameter planes, namely in the (h, T) and (d, T) planes, d is the reduced crystal-field interaction. The phase diagrams always exhibit a tricritical point in (h, T) plane, but do not exhibit in the (d, T) plane for low values of h. The dynamic multicritical point or dynamic critical end point exist in the (d, T) plane for low values of h. Moreover, phase diagrams contain paramagnetic (p), ferromagnetic (f), ferrimagnetic (i) phases, two coexistence or mixed phase regions, (f+p) and (i+p), that strongly depend on interaction parameters.     

Magnetic properties of the bond and crystal field dilution Blume-Emery-Griffiths model in the presence of magnetic field

The magnetic properties of the spin-1 bond and crystal field dilution Blume-Emery-Griffiths (BEG) model in the presence of magnetic field are investigated on a simple cubic lattice by using effective field theory (EFT). In the M-H plane, the common action of bond and crystal field dilution leads to the exhibition of an irregular initial magnetization curve and slows down the magnetization process. The peak of the susceptibility curve has an explicit decline and shows a distinct shift toward the direction of increase of magnetic field. On the other hand, in the M-T plane, the magnetization curves show a discontinuity and a vertical leap in the small range of magnetic field when the negative crystal field is larger and the ratio of biquadratic and exchange interaction is positive (α>0). These results have not been revealed in previous works.     

Dynamics of the one-dimensional random transverse Ising model with next-nearest-neighbor interactions

The dynamics of the one-dimensional random transverse Ising model with both nearest-neighbor (NN) and next-nearest-neighbor (NNN) interactions is studied in the high-temperature limit by the method of recurrence relations. Both the time-dependent transverse correlation function and the corresponding spectral density are calculated for two typical disordered states. We find that for the case of bimodal disorder the dynamics of the system undergoes a crossover from a collective-mode behavior to a central-peak one and for the case of Gaussian disorder the dynamics is complex. For both cases, it is found that the central-peak behavior becomes more obvious and the collective-mode behavior becomes weaker as K_i increase, especially when K_i>J_i/2 (J_i and K_i are the exchange couplings of the NN and NNN interactions, respectively). However, the effects are small when the NNN interactions are weak (K_i<J_i/2).