Critical properties of a random transverse crystal field Ising model with bond dilution

Within effective field theory (EFT), the critical properties of a random transverse crystal field Ising model with bond dilution are studied on a square lattice. Under both weak and strong bond dilution conditions, we consider three cases (α = 0,±0.5) of a transverse crystal field ratio, obtaining global phase diagrams in T−D _x space for changes in the random transverse crystal field concentration. The phase diagrams obtained for a weak bond dilution are very similar in shape to those of pure bond but with decreases in corresponding ordered phases and critical values. However, the phase diagrams for a strong bond dilution exhibit varieties, including a change in reentrant phenomenon, the occurrence of transverse crystal field degeneration, and the opposite direction crossover of temperature peak value.     

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.     

Finite cluster approximation for bond and site dilution transverse ising model on square lattice

The critical behaviour of the bond and site dilution transverse Ising model on a square lattice with spin-1/2 is investigated within the framework of the finite cluster approximation (FCA). The phase diagrams, critical temperature, critical transverse field and percolation threshold are given. The FCA method is conceptually as simple as an ordinary mean field approximation (MFA) but gives much better results.     

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 behaviors of bond and crystal field dilution Blume–Emery–Griffiths model

The critical behavior of the spin-1 bond and crystal field dilution Blume–Emery–Griffiths model have been investigated on simple-cubic lattice within the framework of the effective field theory. In particular, both bond dilution and random crystal field are considered at the same time. The interplay between bond and crystal field dilution constructs rich and interesting phase diagrams. Significant distinctions are exhibited. When positive ratio α changes in a certain range, there exist double tricritical points in phase-transition lines in T–D plane. Moreover, this first-order phase transition is enlarged with increasing of ratio α at a fixed crystal field dilution concentration, while this first-order phase transition will shrink when bond dilution concentration is fixed. In addition, we observe that there exist two bond percolation thresholds for negative crystal field and α>0 in T–P plane.     

Thermodynamic Properties of Random Transverse Field Mixed Spin System in the Presence of Single-Ion Anisotropy

We study the thermodynamic properties of random transverse field mixed spin system in the presence of single-ion anisotropy on a square lattice. By making use of the effective field theory and a cutting approximation, the detailed phase diagrams are described and some interesting results are found under trimodal random transverse field distribution. A small single-ion anisotropy can magnify magnetic ordering region at low temperatures and existence of a large transverse field can assist the occurrence of reentrant phenomena. With increasing disorder, second-order phase transitions are shown to change into first-order phase transitions. The trajectory of the tricritical point in the phase space as a function of disorder is presented. These indicate a strong correlation with the corresponding to trimodal transverse field distribution.     

The spin-

We study the thermodynamic properties of random transverse field mixed spin system in the presence ofsingle-ion anisotropy on a square lattice. By making use of the effective field theory and a cutting approximation, thedetailed phase diagrams are described and some interesting results are found under trimodal random transverse fielddistribution. A smallsingle-ion anisotropy can magnify magnetic ordering region at low temperatures and existence ofa large transverse field can assist the occurrence of reentrant phenomena. With increasing disorder, second-order phasetransitions are shown to change into first-order phase transitions. The trajectory of the tricritical point in the phasespace as a function of disorder is presented. These indicate a strong correlation with the corresponding to trimodaltransverse field distribution.     

Thermodynamic Properties of Random Transverse Field Mixed Spin System in the Presence of Single-Ion Anisotropy

We study the thermodynamic properties of random transverse field mixed spin system in the presence ofsingle-ion anisotropy on a square lattice. By making use of the effective field theory and a cutting approximation, thedetailed phase diagrams are described and some interesting results are found under trimodal random transverse fielddistribution. A smallsingle-ion anisotropy can magnify magnetic ordering region at low temperatures and existence ofa large transverse field can assist the occurrence of reentrant phenomena. With increasing disorder, second-order phasetransitions are shown to change into first-order phase transitions. The trajectory of the tricritical point in the phasespace as a function of disorder is presented. These indicate a strong correlation with the corresponding to trimodaltransverse field distribution.     

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     

The magnetic properties of the two-dimensional square lattice mixed-spin anisotropic Heisenberg ferromagnet with a transverse magnetic field

The two-dimensional square lattice mixed-spin anisotropic Heisenberg ferromagnet with a transverse magnetic field is studied by means of the double-time Green's function. The analytic expressions of the critical temperature, the high-temperature zero-field susceptibilities, the spin-wave velocity, spin-wave stiffness and spin-wave gap are obtained. The phase diagrams in which the critical temperature, the reorientation temperature and the reorientation magnetic field are shown as a function of single-ion anisotropic parameter are discussed.     

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.     

一个镶嵌稀释双键Potts模型的严格解

本文研究在一个镶嵌正方形格子上的一个稀释双键Potts模型,模型中既包含铁磁作用,也包含反铁磁作用。得到了非常一般的和某些特殊情况下的临界行为的严格解及相图。特别是,我们的结果中展示出在二维情况下,当q≤3时,稀释反铁磁Potts模型也如同正规(非稀释)模型一样,存在着特殊的低温相。 关键词：     

Staggered Quadrupolar Phase and Bicritical Point of Spin-1 Bond and Anisotropy Dilution Blume-Emery-Griffiths Model

Within the effective field theory (EFT), staggered quadrupolar phase and bicritical point of spin-1 bond and anisotropy dilution Blume-Emery-Griffiths model is studied on simple cubic lattice in the restricted range of biquadratic interaction and bilinear interaction ratio α≤-1. The phase diagrams present a line of staggered quadrupolar-paramagnetic (SQ-P) phase and a line of ferromagnetic-paramagnetic (F-P) phase, separated by a bicritical point (BCP). A large negative ratio and two different dilution factors magnify the range of the SQ phase and reduce range of ferromagnetic phase in T-α or T-D plane. These parameters can assist the reentrant behavior of the SQ-P line and suppress that of the F-P line. The influence of bond dilution on the BCP is dissimilar to that of anisotropy dilution. There is a degenerate pattern at ground state in T-D plane. Some results obtained by the pure BEG model is in qualitative agreement with the results of Monte Carlo simulations.     

Ferromagnetic Properties of Bond-Dilution and Random Positive or Negative Uniaxial Anisotropy Blume-Capel Model

We study the ferromagnetic properties of spin-1 system, which is considered in the frame of the bond dilution and random positive or negative anisotropy Blume-Capel model in the effective field theory and a cutting approximation. The investigation of phase diagrams displays some rich properties of the trajectory of tricritical point, reentrant henomena at low temperatures. Under certain both bond concentrations and random negative anisotropy, there are new transition lines of double tricritical points. So special emphasis is placed on the influence of the bond dilution and random anisotropy on phase diagrams. The magnetizations of the system are also discussed. Some results have not been evealed in previous reports.     

Magnetic properties of mixed Ising system with random field

A spin-1/2 and spin-3/2 mixed Ising system in a random field is studied by the use of effective-field theory with correlations. The phase diagrams and thermal behaviours of magnetizations are investigated numerically for the honeycomb lattice (z=3) and square lattice (z=4) respectively. The tricritical behaviours for both honeycomb and square lattices, as well as the reentrant behaviour for the square lattice are found.     

Stationary State Solutions of a Bond Diluted Kinetic Ising Model: An Effective-Field Theory Analysis

We examined the stationary state solutions of a bond diluted kinetic Ising model under a time dependent oscillating magnetic field within the effective-field theory (EFT) for a honeycomb lattice (q=3). The effects of the Hamiltonian parameters on the dynamic phase diagrams have been discussed in detail. Bond dilution process on the kinetic Ising model causes a number of interesting and unusual phenomena such as reentrant phenomena and has a tendency to destruct the first-order transitions and the dynamic tricritical point. Moreover, we have investigated the variation of the bond percolation threshold as functions of the amplitude and frequency of the oscillating field.     

The spin-2 antiferromagnet on the Bethe lattice

The complete phase diagrams of the antiferromagnetic spin-2 Blume-Capel Ising system is studied on the Bethe lattice by the use of exact recursion relations. In order to specify the states of the system, i.e. the different spin configurations, the ground state phase diagram is obtained on the (H/|J|, D/|J|) plane corresponding to the reduced external magnetic and crystal fields, respectively. As a result, the thermal change of the order-parameters, the magnetisations belonging to the two sublattice system, was investigated to obtain the full phase diagrams of the system on the (H/|J|, kT/|J|) planes. The behavior of the order-parameters with respect to the external magnetic field was also studied for the given values of D/|J|. Besides the interesting thermal and external magnetic field change of the sublattice magnetisations, the system also exhibits interesting critical behaviors including first- and second-order phase transitions, therefore, triciritical points and the reentrant behavior. The calculations are carried out for the coordination number q=4, corresponding to the square lattice, only.     

Ground-state magnetic properties of the spin-2 transverse Ising model

The ground-state magnetic properties of the spin-2 transverse Ising model with a longitudinal crystal field are studied within the framework of mean-field theory (MFT) and effective-field theory (EFT), respectively. The phase diagrams and magnetization curves are examined in detail. It is found that the system exhibits a tricritical behavior in the ground-state phase diagrams. Some interesting phenomena have been found, especially the first-order phase transition from one ordered phase to the other ordered phase, which is due to the high spin. The spin correlation has important effect on the magnetic properties of the system. We also find that the ground-state phase diagrams of the spin-2 transverse Ising model are very different from those of the spin-3/2 transverse Ising model.