Magnetic properties of a mixed spin-1 and spin-2 Heisenberg ferrimagnetic system: Green’s function study

The magnetic behaviors of a mixed spin-1 and spin-2 Heisenberg ferrimagnetic system on a square lattice are studied by using the double-time temperature-dependent Green’s function technique. In order to decouple the higher order Green’s functions, Anderson and Callen’s decoupling and random phase approximations have been used. The system is described in the presence of an external magnetic field. We illustrate the influences of the nearest- and next-nearest-neighbor interactions and the single-ion anisotropies with an external magnetic field on compensation and critical temperatures. We found that the system that includes only the nearest-neighbor interaction and the single-ion anisotropies does not have a compensation temperature. When the next-nearest-neighbor interactions exceed a certain minimum value, a compensation temperature begins to appear. For some negative values of single-ion anisotropies, there exist first-order phase transitions. The system has first-order phase transition properties when it is under the influence of an external magnetic field.     

Spin compensation temperatures in the mean-field approximation of a mixed spin-2 and spin-5/2 Ising ferrimagnetic system

The magnetic behaviors of a mixed spin-2 and spin-5/2 Ising ferrimagnetic system on a square lattice are studied with the mean-field approximation (MFA) based on the Bogoliubov inequality for the free energy. A Landau expansion of the free energy in the order parameter is also described in this work. In particular, we investigate the effect of a single-ion anisotropy on the compensation phenomenon.     

Random crystal-field effects in a mixed spin-1/2 and spin-2 ferrimagnetic Ising system

The magnetic properties of a mixed spin ferrimagnetic system σ?=?1/2 and S?=?2 at the sites of a square lattice with a random crystal field are studied by the mean field approximation. The ground state of the system is determined and the total magnetization is plotted according to the model parameters. Different behaviors for the thermal dependence of the magnetization are highlighted. In particular, one sees the appearance of one or two compensating points and many types of phase diagrams with first and second order phase transition lines as well as isolated critical and tricritical points.     

Spin compensation temperatures induced by longitudinal fields in a mixed spin-3/2 and spin-5/2 Ising ferrimagnet

I studied the ferrimagnetic Ising model with nearest neighbour interactions for a square lattice and simple cubic one, using mean field theory. The free energy of a mixed spin Ising ferrimagnetic model was calculated from a mean field approximation of the Hamiltonian. By minimizing the free energy, I obtained the equilibrium magnetizations and the compensation temperatures. Clear indications of the single-ion anisotropies on the compensation points of the mixed spin-3/2 and spin-5/2 ferrimagnetic lattices are found. Some interesting behaviors of these systems are obtained depending not only on the values of magnetic anisotropies for both sublattice sites but also on the lattice structure. The longitudinal magnetic fields dependence of the spin compensation temperature is the main focus of research. The possibility of many compensation temperatures is indicated.     

Magnetic Properties of a Mixed Spin-2 and Spin-5/2 Heisenberg Ferrimagnetic System on a Two-Dimensional Honeycomb Lattice： Green＇s Function Approach

The multisublattice Green＇s function technique is applied to study the magnetic properties of a mixed spin-2 and spin-5/2 Heisenberg ferrimagnetic system on a two-dimensional honeycomb lattice. The role of the different interactions in the Hamiltonian is explored. When only the nearest-neighbor interaction and the single-ion anisotropy are included, our results indicate that there are compensation points at finite temperatures. When the next-nearest-neighbor interaction exceeds a minimum value that depends on the other parameters in the Hamiltonian, the compensation point disappears. The next-nearest-neighbor interaction has the effect of changing the compensation temperature.     

Thermal and magnetic properties of a ferrimagnetic nanoparticle with spin-3/2 core and spin-1 shell structure

Intensive Monte Carlo simulations based on standard Metropolis algorithm have been applied to investigate the phase diagrams of a ferrimagnetic cubic nanoparticle (nanocube) with a spin-3/2 core surrounded by a spin-1 shell layer with antiferromagnetic interface coupling. It has been shown that occupation of sites of particle core by spin-3/2 plays an important role on the shape of the phase diagrams. In addition, effects of the crystal field interaction as well as exchange interactions on the thermal and magnetic properties of the system have also been discussed in detail, and some interesting features have been observed for the temperature dependence of total magnetization curves of particle.     

Thermodynamic properties of the mixed spin-1/2 and spin-1 Ising chain with both longitudinal and transverse single-ion anisotropies

The mixed spin-1/2 and spin-1 Ising chain with both longitudinal and transverse single-ion anisotropies is solved exactly by means of a mapping to the spin-1/2 Ising chains with alternating transverse fields and the Jordan-Wigner transformation. Within this scheme, the thermodynamic quantities of this model are rigorously determined by a recursion formula derived for the partition function based on the reduced spin-1/2 transverse Ising model. The corresponding thermodynamic properties are calculated and discussed.     

Three-dimensional static Green's function for a half space over mixed PEC and dielectric wedges

A pseudo-analytical solution technique is proposed to determine the three-dimensional static Green's function for a half space over mixed perfect electric conductor-dielectric wedges. The governing Poisson's equation is solved, using the Kontorovich–Lebedev and Fourier transforms. The solution, expressed in terms of image contributions, consists of an excitation point source, a set of point images in physical space, and two line images located in complex space for each region of the problem geometry. The validity of the proposed technique is confirmed by comparing our results with the existing analytical solutions and those obtained numerically using the using a finite integration code.     

Exact results of an alternating-bond mixed spin-1/2 and spin-1 Ising chain with both longitudinal and transverse single-ion anisotropies

The alternating-bond mixed spin-1/2 and spin-1 Ising chain with both longitudinal and transverse single-ion anisotropies are solved exactly by means of a mapping of the spin-1/2 transverse Ising chain and the Jordan-Wigner transformation. The ground state quantities are strongly dependent on the model Hamiltonian parameters J₁, J₂, D_x and D_z. We obtain the quasi-particles' spectra Λ_k, the dimerization gap Δ_d, the minimal energy Δ₀ for exciting a fermion quasi-particle, the minimal energy gap Δ_h for exciting a hole and the ground state energy E_g. The phase diagram of the ground state is also given. The results show that the alternating bond just quantitatively changes the ground state properties; no matter the nearest-neighbor exchange interactions J₁ and J₂ are equal or not, when D_z≥0 for any finite value of D_x, there is no quantum critical point and the ground state is always in a spin ordered phase.     

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.     

阻挫诱导的亚铁磁性Heisenberg系统中的量子相变

利用密度矩阵重整化群(DMRG)方法研究磁性阻挫对一种S=1/2准一维反铁磁自旋链但却具有亚铁磁性的Heisenberg系统基态的影响.计算了单个晶胞的基态能、自旋关联函数以及自旋能隙.研究表明这种Heisenberg自旋系统的基态随着阻挫α的增强将从磁有序相变化到自旋无序相，并且伴随着自旋能隙的出现，量子相变点为α≈0.412.同时线形链上格点间自旋长程关联值的计算结果表明在磁有序区间体系的磁有序性质随着α的增强而减弱，阻挫在0≤α<     

阻挫诱导的亚铁磁性Heisenberg系统中的量子相变

利用密度矩阵重整化群(DMRG)方法研究磁性阻挫对一种S=1/2准一维反铁磁自旋链但却具有亚铁磁性的Heisenberg系统基态的影响.计算了单个晶胞的基态能、自旋关联函数以及自旋能隙.研究表明这种Heisenberg自旋系统的基态随着阻挫α的增强将从磁有序相变化到自旋无序相,并且伴随着自旋能隙的出现,量子相变点为α≈0.412.同时线形链上格点间自旋长程关联值的计算结果表明在磁有序区间体系的磁有序性质随着α的增强而减弱,阻挫在0≤α< 关键词： 准一维反铁磁自旋链 亚铁磁性 密度矩阵重整化群 自旋能隙     

Calculation of correlation functions in the Heisenberg spin-1/2 antiferromagnetic model

We derive the exact expression of the four-spinon contribution S ₄ to the dynamical correlation function S of the spin 1/2 isotropic (XXX) He isenberg model in the antiferromagnetic regime using the quantum group symmetry of the model. We first give the exact expression for the n-spinon contribution in the form of contour integrals and display known results regarding the two-spinon contribution S ₂. Then we specialize the n-spinon formula to the case n = 4 and compute three sum rules for S ₄ that the total S is known to satisfy exactly. These are: the total integrated intensity, the first frequency moment and the nearest-neighbor correlation function. We find that S ₄ corrects only by a small amount the contribution from S ₂. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

The Green's function of the Poisson equation on the non-concentric annular region

In this article the two-dimensional Poisson equation is considered in the region between two non-concentric circular cylinders. Upon introducing bipolar coordinates the corresponding Green's function is found in form of a simple and rapidly converging series which can be formally summarized as a closed-form. Based on this result we additionally provide the Green's function for the conducting cylinder which is oriented parallel to a ground plane as well as for the case of two conducting cylinders.     

Properties of advanced coupled-cluster Green's function

ABSTRACT

We present an extension of the analysis previously applied to the retarded part of the coupled cluster (CC) Green's function to its advanced part. In analogy to our earlier studies for the retarded part, we demonstrate that the advanced CC Green's function is expressed in terms of connected diagrams only, which is a direct consequence of algebraic form of equations satisfied by CC amplitudes. We also demonstrate that ω-derivatives of the advanced CC Green's function can be calculated analytically and can be expressed in terms of connected diagrams only. We analyse the structure of connected diagrams and the role of intermediate operators which satisfy electron affinity equation-of-motion CC-type conditions.     

Random crystal field effect on hysteresis loops and compensation behavior of mixed spin-(1, 3/2) Ising system

Magnetic hysteresis and compensation behavior of a mixed spin-(1, 3/2) Ising model on a square lattice are investigated in the framework of effective field theory based on a probability distribution technique. The effect of random crystal field, ferromagnetic and ferrimagnetic exchange interaction on hysteresis loops and compensation phenomenon are discussed. A number of characteristic phenomena have been reported such as the observation of triple hysteresis loops at low temperatures and for negative values of random crystal field. Critical and double compensation temperatures have been also found. The obtained results are also compared to some previous works.     

The Green's function of confined electrons in an external magnetic field: Analytical formulation

We derive the analytical form of the Green's function of 2-dimensional electrons with lateral confinement in a perpendicular magnetic field. The confinement potentials considered are infinite barriers at radius R (quantum dot) and at r and R (quantum ring).     

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.     

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.