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     

次近邻作用对随机量子Ising系统动力学性质的影响

利用递推关系方法在高温极限下研究了具有次近邻自旋耦合相互作用的一维随机量子Ising系统的动力学性质,求解了系统的自关联函数及谱密度.假设自旋耦合参量或横向磁场满足双高斯分布,研究发现当随机变量的标准偏差σJ(σB)较小时系统的动力学性质存在从集体模行为到中心峰值行为的交跨效应,当σJ(σB)较大时,交跨效应消失,系统只表现一种动力学行为.讨论了次近邻相互作用对系统动力学性质的影响,发现当KiJ2i(Ji和Ki分别为近邻和次近邻相互作用)时次近邻相互作用对系统动力学性质的影响不太明显,可以忽略;当Ki2Ji时,次近邻相互作用使得系统的中心峰值行为表现得更加明显,或使其集体模行为呈减弱的趋势.     

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     

Magnetic properties in a transverse Ising nanowire with an antiferromagnetic spin configuration at the surface

The phase diagrams and temperature dependences of magnetizations in a transverse Ising nanowire with an antiferromagnetic spin configuration at the surface are studied by the use of the effective-field theory with correlations. A number of characteristic features, such as the possibility of reentrant phenomena being free from disorder-induced frustration, are obtained for the magnetic properties in the system.     

Ferroelectricity in a diatomic Ising chain as investigated by the elastic Ising model

An elastic Ising model for a one-dimensional diatomic spin chain is proposed to explain the ferroelectricity induced by the collinear magnetic order with a low-excited energy state. A statistical theory based on this model is developed to calculate the electrical and magnetic properties of Ca₃CoMnO₆, a typical quasi-one-dimensional diatomic spin chain system. The calculated ferroelectric polarization and dielectric susceptibility show a good agreement with recently reported data on Ca₃Co_2-xMn_xO₆ (x ≈0.96) (Phys. Rev. Lett. 100 047601 (2008)), although the predicted magnetic susceptibility does not coincide well with experiment. We also address the rationality and deficiency of this model by including a first-order correction which improves the consistency between the model and experiment.     

The transverse spin-1 Ising model with random interactions

The phase diagrams of the transverse spin-1 Ising model with random interactions are investigated using a new technique in the effective field theory that employs a probability distribution within the framework of the single-site cluster theory based on the use of exact Ising spin identities. A model is adopted in which the nearest-neighbor exchange couplings are independent random variables distributed according to the law P(J_ij)=pδ(J_ij−J)+(1−p)δ(J_ij−αJ). General formulae, applicable to lattices with coordination number N, are given. Numerical results are presented for a simple cubic lattice. The possible reentrant phenomenon displayed by the system due to the competitive effects between exchange interactions occurs for the appropriate range of the parameter α.     

Mixed spin Ising model with four-spin interaction and random crystal field

The effects of fluctuations of the crystal field on the phase diagram of the mixed spin-1/2 and spin-1 Ising model with four-spin interactions are investigated within the finite cluster approximation based on a single-site cluster theory. The state equations are derived for the two-dimensional square lattice. It has been found that the system exhibits a variety of interesting features resulting from the fluctuation of the crystal field interactions. In particular, for low mean value D of the crystal field, the critical temperature is not very sensitive to fluctuations and all transitions are of second order for any value of the four-spin interactions. But for relatively high D, the transition temperature depends on the fluctuation of the crystal field, and the system undergoes tricritical behaviour for any strength of the four-spin interactions. We have also found that the model may exhibit reentrance for appropriate values of the system parameters.     

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.     

The possibility of re-entrant phenomena induced by a transverse field in ultra-thin transverse Ising films

The phase diagrams and temperature dependences of magnetizations in ultra-thin transverse Ising thin films are studied by the use of both the effective-field theory with correlations (EFT) and the mean-field theory (MFA). Novel features, such as the possibility of re-entrant phenomena, are obtained for the magnetic properties in such systems with a zero transverse field at the surfaces, when the EFT is applied to them, although such features could not be found from the use of the MFA. When the transverse field at the surfaces takes a finite value, however, the re-entrant phenomena could not be found from the both formulations of the EFT and the MFA. Similar phenomena are then obtained in the phase diagrams by using the MFA and the EFT.     

Enhancement of next-nearest-neighbouring entanglement in quantum Ising spin chain

Using the method of the Jordan--Wigner transformation for solving different spin--spin correlation functions, we have investigated the generation of next-nearest-neighbouring entanglement in a one-dimensional quantum Ising spin chain with the Gaussian distribution impurities of exchange couplings and external magnetic fields taken into account. The maximal value of entanglement between the next-nearest-neighbouring qubits in the transverse Ising model was analysed in detail by varying the effectively controlled parameters such as interchange coupling, magnetic field and the system impurity. For such systems, where both exchange couplings and external magnetic field disorder appear, we show that it is possible to achieve next-nearest-neighbouring entanglement better than the previously discussed pure Ising spin chain case. We also show that the Gaussian distribution impurity can induce next-nearest-neighbouring entanglement, which can be used as a means to characterize quantum phase transition.     

On the nonergodicity of the transverse magnetization in the transverse Ising model

The nonergodic behavior exhibited by the transverse spin correlation function _q=0 ^xx (t) the transverse Ising model obtained as the solution of approximate kinetic equations (derived on the basis of Résibois and De Leener's method), is shown to be an intrinsic property of the model and not the result of the approximations made in the derivation of the kinetic equations.Chargé de Recherches au Fonds National Belge de la Recherche Scientifique.     

Some properties of random Ising models

We consider an Ising model with random magnetic fieldh _i and random nearest-neighbor couplingsJ _ij . The random variablesh _i andJ _ij are independent and identically distributed with a nice enough distribution, e.g., Gaussian. We will prove that (i) at high temperature, infinite volume correlation functions are independent on the boundary conditions and decay exponentially fast with probability 1 and (ii) for any temperature with sufficiently strong magnetic field the correlation functions are again independent on the boundary conditions and decay exponentially fast with probability 1. We also prove that the averaged magnetization of the ground state configuration of the one-dimensional Ising model with random magnetic field is zero, no matter how small is the variance of theh _i .     

Frustration in a transverse Ising nanoisland: effects of interlayer coupling

The phase diagram and magnetizations in a transverse Ising nanoisland are examined by using the effective field theory with correlations. The nanoisland is constructed from two layers with nine atoms in each which are coupled by the interlayer coupling. We present some characteristic phenomena in them which come from the frustration induced by an interlayer coupling and two transverse fields.     

Some characteristic phenomena in a transverse Ising nanotube

The phase diagram and magnetizations of a cylindrical nanotube described by the transverse Ising model are investigated by the use of the effective field theory with correlations. Some comparisons between the nanotube and the nanowire have been given for the phase diagrams. In particular, the temperature dependences of longitudinal magnetization in the system with a negative shell–core interaction are investigated. Some characteristic phenomena (new types in ferrimagnetism) which have not been observed in the nanowire as well as similar phenomena are found in the thermal variations, depending on the ratio of the physical parameters in the surface shell and the core. The possibilities of two compensation points and a field induced compensation point in the nanotube are also discussed.     

Decay of the remanent magnetization in the asymmetric spin chain

The dynamics of the one-dimensional spin glass with asymmetric interactions between neighboring spins is considered. We confine ourselves to discrete couplings with values ±J. We show that the algebraic decay of the remanent magnetization of the infinite ±J-spin chain at zero temperature is only valid for symmetric couplings. Our analytical investigations as well as computer simulations show stretched exponential decay for any finite concentration of antisymmetric bonds. Thus, the asymmetric ±J-spin chain shows an asymmetry-induced phase transition at zero temperature.     

Mixed spin transverse Ising model with longitudinal random crystal field interactions

The effect of a longitudinal random crystal field interaction on the phase diagrams of the mixed spin transverse Ising model consisting of spin-1/2 and spin-1 is investigated within the finite cluster approximation based on a single-site cluster theory. In order to expand a cluster identity of spin-1, we transform the spin-1 to spin-1/2 representation containing Pauli operators. We derive the state equations applicable to structures with arbitrary coordination number N. The phase diagrams obtained in the case of a honeycomb lattice (N=3) and a simple-cubic lattice (N=6), are qualitatively different and examined in detail. We find that both systems exhibit a variety of interesting features resulting from the fluctuation of the crystal field interactions. Received: 13 February 1998 / Accepted: 17 March 1998     

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.     

Relaxation times in a finite Ising system with random impurities

Finite-size scaling effects of the Ising model with quenched random impurities are studied, focusing on critical dynamics. In contrast to the pure Ising model, disordered systems are characterized by continuous relaxation time spectra. Dynamic field theory is applied to compute the spectral densities of the magnetizationM(t) and ofM ²(t). In addition, universal cumulant ratios are calculated to second order in ^1/4, where =4–d andd<4 denotes the spatial dimension.