The spin-

The magnetic properties of bond-diluted nearest-neighbor interaction mixed spin-1/2 and spin-1 Ising ferrimagnetic spin system with different transverse fields are investigated within the framework of the finite cluster approximation (FCA). Particular emphasis is given to the square lattice with coordination number 2 = 4 for which magnetizations are obtained. The interactions Jij are assumed to be independent random variable with distribution P(J_ij) = pδ(J_ij-J) + (1-p)δ(J_ij), where J < 0. If bond concentration p varies in the certain ranges, we find that the compensation temperature is obtained for the values of the different transverse fields Ω_1/2 and Ω₁ in a restricted region. We obtain the values of the critical different transverse fields and critical bond concentration in this paper.     

A Compensation Temperature Study of Bond-Diluted Mixed Ising Ferrimagnetic Spin System with Different Transverse Fields

The magnetic properties of bond-diluted nearest-neighbor interaction mixed spin-1/2 and spin-1 Ising ferrimagnetic spin system with different transverse fields are investigated within the framework of the finite cluster approximation (FCA). Particular emphasis is given to the square lattice with coordination number 2 = 4 for which magnetizations are obtained. The interactions Jij are assumed to be independent random variable with distribution P(J_ij) = pδ(J_ij-J) + (1-p)δ(J_ij), where J < 0. If bond concentration p varies in the certain ranges, we find that the compensation temperature is obtained for the values of the different transverse fields Ω_1/2 and Ω₁ in a restricted region. We obtain the values of the critical different transverse fields and critical bond concentration in this paper.     

随机横场与晶场作用混合自旋系统的热力学性质

利用有效场理论和切断近似，在伊辛模型的框架内考虑随机横场与晶场作用的混合自旋1/2 和自旋1系统的热力学性质。重点研究了晶场、横场和随机浓度对混合自旋系统相变的影响 ，研究发现在随机横场条件下，较小的晶场存在并不能改变临界横场阈值；取较大横场值时 在某些随机浓度的范围内出现重入相变现象，而取较小横场值时则没有出现重入相变现象。 给出了有关相图并进行了讨论。 关键词： 混合自旋系统 伊辛模型 热力学性质 随机横场     

Thermodynamical properties of the transverse Ising model

A new effective field theory is proposed and used to derive the thermodynamical properties of the transverse Ising model. The formalism is based on an exact formal spin identity for the two-state transverse Ising model and utilizes an exponential operator technique. The method, which can explicitly and systematically include correlation effects, is illustrated in several lattice structures by employing its simplest approximation version (in which spin-spin correlations are neglected). The lines of critical points in the Ω-T plane as well as the thermal behaviour of both transverse and longitudinal magnetizations are analysed for square and simple cubic lattices. It is shown that the present formalism, in spite of its simplicity, yields results which represent a remarkable improvement on the standard mean field treatment (MFA).     

Weakly nonparaxial spatial optical solitons in different mechanisms of Kerr nonlinearity

The structure of spatial (two-dimensional transverse) weakly nonparaxial solitons is determined by solving the Maxwell equations for a medium characterized by different mechanisms of Kerr (cubic) nonlinearity in the approximation of beams with a width greatly exceeding the wavelength of light. Two modes are distinguished for these solitons: a trapping mode, with a constant transverse field profile, and a beating mode, with longitudinal oscillations of the field structure. The angular structure of the field in the beating mode (which is realized when the radiation power slightly exceeds the critical power of self-focusing) is determined.     

Fermionic Ising glasses in magnetic transverse field with BCS pairing interaction

We study a fermionic infinited-ranged Ising spin glass with a real space BCS interaction in the presence of an applied transverse field. The problem is formulated in the integral functional formalism where the SU(2) spins are given in terms of bilinear combinations of Grassmann fields. The problem is solved within static approximation and the replica symmetry ansatz combined with previous approaches used to study the critical behavior of the quantum Ising spin glass in a transverse field and the spin glass Heisenberg model with BCS pairing. Our results show that the transverse field has strong effect in the phase boundary of the spin glass phase and the PAIR phase in which there is a long range order corresponding to formations of pairs. The location of the tricritical point in the PAIR phase transition line is also affected.     

横向随机晶场Ising模型的相图和磁化行为研究

在有效场理论和切断近似框架内，选择自旋S=1的二维方格子，研究横向随机晶场Ising模型的相图和磁化行为，重点是横向随机晶场浓度和晶场比率对相图和磁化的影响.给出了i>T-D_x空间的相图和m-T空间的磁化图.在晶场稀疏情况下，负晶场方向存在临界温度的峰值，正方向可出现重入现象.晶场比率取+0.5和-0.5时，磁有序相范围缩小，特别是晶场比率取-0.5时，随晶场浓度的降低，临界温度峰值从横向晶场负方向渡越到正方向.固定某一负晶场值，不同晶场比率的磁化行为有明显差异.同时与纵向稀疏晶场Ising模型结果进行有意义的比较. 关键词： 横向随机晶场Ising模型 相图 磁化行为     

Critical Properties of Mixed Ising Spin System with Different Trimodal Transverse Fields in the Presence of Single-Ion Anisotropy

Within the framework of an effective field approximation, the effects of single-ion anisotropy and different trimodal transverse fields of two sublattices on the critical properties of the mixed spin-1/2 and spin-1 Ising system are investigated on the simple cubic lattice. A smaller single-ion anisotropy can magnify magnetic ordering phases and a larger one can depress magnetic ordering phase for T-Ω_1/2 space at low temperatures, while a smaller single-ion anisotropy can hardly change the value of critical transverse field for T-Ω₁ space. On the other hand, influences of two different trimodal transverse fields concentrations on tricritical points and magnetic ordering phases take on some interesting results in T-D space. The main reason comes from the common action of single-ion anisotropy, different transverse fields and two trimodal distributions.     

Trimodal random-field spin- Ising systems in a transverse field

The trimodal random-field spin- Ising system in a transverse field is investigated by combining the pair approximation with the discretized path-integral representation by introducing a parameter p to simulate the fractions of the spins not exposed to the external longitudinal magnetic field. The variation of the critical reduced transverse field and longitudinal magnetic field with the parameter p is studied for different coordination numbers and it is found that the system does not exhibit any tricritical points for p>0.22. The phase diagrams with respect to the external longitudinal random-field and the second-order phase transition temperature are obtained for given values of the transverse field, coordination numbers and the parameter p. It is found that for appropriate values of the system parameters the system does present tricritical points and reentrant phase transitions, which may be caused by the competition between the quantum effects and randomness.     

Bandgap tuning in armchair MoS(2) nanoribbon

We report on the first-principles calculations of bandgap modulation in armchair MoS(2) nanoribbon (AMoS(2)NR) by transverse and perpendicular electric fields respectively. In the monolayer AMoS(2)NR case, it is shown that the bandgap can be significantly reduced and be closed by transverse field, whereas the bandgap modulation is absent under perpendicular field. The critical strength of transverse field for gap closure decreases as ribbon width increases. In the multilayer AMoS(2)NR case, in contrast, it is shown that the bandgap can be effectively reduced by both transverse and perpendicular fields. Nevertheless, it seems that the two fields exhibit different modulation effects on the gap. The critical strength of perpendicular field for gap closure decreases with increasing number of layers, while the critical strength of transverse field is almost independent of it.     

The quantum transverse spin-2 Ising model with a bimodal random-field in the pair approximation

In this paper, we have investigated the bimodal random-field spin-2 Ising system in a transverse field by combining the pair approximation with the discretized path-integral representation. The exact equations for the second-order phase transition lines and tricritical points are obtained in terms of the random field H, the transverse field G and the coordination number z. It is found that there are some critical values for H and G where the tricritical points disappear for given z. We have also observed that the system presents reentrant behavior which may be caused by the quantum effects and randomness. The phase diagram with respect to the random field and the second-order phase transition temperature are studied extensively for given values of the transverse field and the coordination number.     

An introduced effective-field theory study of spin-1 transverse Ising model with crystal field anisotropy in a longitudinal magnetic field

A spin-1 transverse Ising model with longitudinal crystal field in a longitudinal magnetic field is examined by introducing an effective field approximation (IEFT) which includes the correlations between different spins that emerge when expanding the identities. The effects of the crystal field as well as the transverse and longitudinal magnetic fields on the thermal and magnetic properties of the spin system are discussed in detail. The order parameters, Helmholtz free energy, entropy and specific heat curves are calculated numerically as functions of the temperature and Hamiltonian parameters. A number of interesting phenomena such as reentrant phenomena originating from the temperature, crystal field, transverse and longitudinal magnetic fields have been found.     

Numerical simulation of magnetization process in antiferromagnetic–ferromagnetic bilayer with compensated interface

The properties of antiferromagnetic (AFM)–ferromagnetic (FM) bilayer have been studied using self-consistent mean-field approximation for Heisenberg Hamiltonian. The perpendicular exchange coupling has been revealed in a bilayer with a compensated interface. For a uniform AFM film a symmetrical hysteresis loop has been calculated, because the transverse instability develops within the AFM film at certain critical value of external magnetic field. On the other hand, shifted hysteresis loop with a finite exchange bias field has been obtained for a non-uniform AFM film consisting of various AFM domains with perpendicular directions of the easy anisotropy axes.     

Effects of the bond dilution on the phase diagrams of a spin-1 transverse Ising model with crystal field interaction on a honeycomb lattice

A bond diluted spin-1 Ising model with crystal and transverse field interactions is examined for honeycomb lattice by introducing an effective field approximation that takes into account the correlations between different spins that emerge when expanding the identities. The effects of the crystal field as well as the transverse field and dilution on the phase diagrams and order parameter m_z are discussed in detail. A number of interesting and unusual phenomena such as reentrant phenomena and three successive phase transitions originating from the crystal field as well as the transverse field and bond dilution have been found.     

Crystal-Field Effect of spin-3/2 Transverse Ising Model

The crystal-field effect of spin-3/2 transverse Ising model is studied with the scheme of mean-field approximation. The influences of the crystal field and the transverse field on the phase diagram of the system are discussed.     

Optical bistabilities of higher harmonics: Inhomogeneous and transverse effects

The steady state behavior of optical bistable system in a ring cavity with transverse field variations and inhomogeneousely broadened two-level atoms is investigated outside the rotating wave approximation (RWA). Analytical and numerical investigation is presented for different cases of transverse field variations with Lorentzian or Gaussian line widths. When both (transverse and inhomogeneous) features taken into account, the first harmonic output field component outside the RWA exhibits a one-way switching down processes (butterfly OB) or reversed (clockwise) OB behavior, depending on the atomic linewidth shape.     

Energy flux of a Gaussian beam in microwave band beyond the paraxial approximation

Through the analytic method beyond the paraxial approximation, the energy flux for the general fields of a Gaussian laser beam in microwave band (∼10⁸–10¹⁰ Hz) with different diffraction angles and longitudinal positions are derived. The results indicate a Gaussian beam (GB) has a certain number of transverse energy flux, and it would be enhanced with larger diffraction angle. In the range of beyond paraxial approximation, the transverse flux plays an important role in energy distribution, so that it cannot be ignored when the GB is highly focused. Meanwhile both transverse and longitudinal energy decay along the propagation direction, and the proportion of transverse energy far from beam axis is much more than the counterpart in paraxial area. The transverse energy as mainly characteristic of GB will be much useful for the interactions between electromagnetic field and other field.     

Pair Approximation Method Applied to a Quantum Transverse Ising Spin-Glass Model

The quantum version of the Sherrington-Kirkpatrick model in a transverse field is investigated by combining the pair approximation with the discrete path-integral representation. The free energy and the field-dependent freezing temperature T_c(Г) of the model are obtained,and the classical result for the vanishing of the transverse field (Г → 0) can be reproduced.