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     

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.     

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.     

Phase transition features of the bond-dilution transverse ferromagnetic Ising spin system with random crystal field

The bond dilution spin-1 transverse ferromagnetic Ising model with random crystal field is investigated in the framework of effective field theory (EFT). The general expressions of magnetization are derived for lattice with any coordination number z. In particular, we calculate the phase diagrams of a square lattice. The second-order phase transition lines and the tricritical points are presented in different conditions for the square lattice. Special emphasis is placed on the influence of bond dilution, random crystal field and the transverse field on the phase diagrams. We discover some unusual phenomena. New results obtained in this paper are discussed in detail.     

The bicritical phase diagram of two-dimensional antiferromagnets with and without random fields

Neutron scattering measurements have been made of the phase diagrams of the nearly two-demensional antiferromagnets Rb₂MnF₄ and Rb₂Mn_0.7Mg_0.3F₄ in a magnetic field applied along thec-axis. In Rb₂MnF₄ there is at low temperatures a spin-flop phase at fields above 5.5 T which has long range order. The observation of true long range order rather than the algebraic decay of the order characteristic of the two-dimensional XY model is presumably due to subtle anisotropy effects in the plane as well as weak three-dimensional coupling. The phase boundaries of the uniaxial and transverse phases are shown to be consistent with renormalization group predictions for two-dimensional systems. The two lines become exponentially close to each other at low temperatures. The weak three-dimensional coupling moves the bicritical point fromT=0 to a non-zero temperature. The situation is more complex in Rb₂Mn_0.7Mg_0.3F₄ because of Ising random field effects. At low fields we observe typical random field metastable behavior with a sharp metastability boundary and a gange of length scales which are time independent below that boundary. At higher fields there are substantial uniaxial fluctuations. The transverse phase boundary and the metastability line appear to intercept atT=0 showing that the random field fluctuations do have a large effect on the phase diagram. The theory of the phase diagrams has been extended to include the random field fluctuations and good agreement is obtained with the observed transverse phase boundary. Unfortunately, there is as yet no theory of the metastable uniaxial phase with which to compare our results.     

Critical behavior of a degenerate ferromagnet in a uniaxial random field: Exact results in a space of arbitrary dimension

The critical behavior of the transverse (with respect to the field) magnetization component in classical degenerate magnets with only nearest-neighbors interaction in a uniaxial random magnetic field at zero temperature is found exactly. For a Gaussian distribution of the random field the asymptotic transverse magnetization in strong fields does not depend on the dimension of the space and is of the form m _⊥ ∝ 1nh ₀/h ₀ ² , where h ₀ is the width of the distribution. For a bimodal distribution, where only the field direction is random and the amplitude is fixed, the transverse magnetization behaves as m _⊥∝exp(−const/(H _c −H) ^D/2), where H is the amplitude of the random field, D is the dimension of the space, and H _c is the critical field. Zh. éksp. Teor. Fiz. 115, 2143–2159 (June 1999)     

Phase transition properties of the spin-1 Blume-Emery-Griffiths model with random transverse crystal field

Phase transition properties of a spin-1 Blume-Emery-Griffiths model (BEGM) with random transverse crystal field is studied by the effective field theory for a simple cubic lattice. In T−D_x space, we obtain the phase diagrams with the ratio α between the biquadratic interaction and the exchange interaction as well as a tunable parameter l of the transverse crystal field. The tricritical point (TCP) appears at α<0, which undergoes a crossover from positive to negative direction of the transverse crystal field when l<0. The TCP cannot be observed for α>0. The maximum critical temperature increases with the increase of α. The position of the peak value tends to the drift of negative or positive direction for a different magnitude or an imperfect (±) transverse crystal field distribution. In T−α space, the range of ordered phase is magnified when the ratio is changed from α<0 to α>0. The random transverse crystal field obviously affects the TCP.     

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.     

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     

Influence of the electric field on structural transformations and phase boundary for PMg1/3Nb2/3O3-xPbTiO3 single crystals

The influence of different regimes of application of a dc electric field (0 < E < 4 kV/cm) on structural phase transformations and behavior of the phase boundary in [001]-oriented single crystals PMg_1/3Nb_2/3O₃-xPbTiO₃ (PMN-xPT) with compositions near the morphotropic phase boundary (x = 28 and 32%) and far from it (x = 13%) has been investigated. The studies have been performed using optical methods, namely, optical transmittance and small-angle light scattering. It has been revealed that the number, symmetry, and stability of field-induced phases depend on the regime of electric field application. During cooling of the PMN-28PT crystals from the cubic phase in the field (FC regime), the tetragonal phase is induced already in weak fields of ∼0.5 kV/cm, whereas even a field of 3 kV/cm is insufficient for inducing this phase by applying the field in the ferroelectric phase. In the PMN-32PT crystal (which has a composition closer to the morphotropic phase boundary as compared to that of the PMN-28PT crystal) in the FC regime and when the field is applied in the ferroelectric phase, the tetragonal phase is induced already in weak electric fields, even though this phase in the latter case appears to be unstable. The E-T phase diagrams have been constructed for different regimes of field application. The possible factors responsible for the observed differences have been discussed.     

The effect of a magnetic field on Jahn-Teller ordering in the monoclinic crystal RbDy(WO4)2

This paper presents the results of a study of the thermal properties of monoclinic single-crystal RbDy(WO₄)₂ at temperatures of 2–15 K and in magnetic fields up to 6 T. From the results of measurements of the heat capacity and thermograms, two structural phase transitions are detected, at T _c1=4.9 K and T _c2=9.0 K. The transformation from the high-temperature phase to the low-temperature phase occurs via an intermediate phase. The field dependences of the critical temperatures are found for various magnetic-field orientations. H-T phase diagrams are constructed for H‖a and H‖c. An anomalous increase (by almost an order of magnitude) of the relaxation time of the system, associated with structural instability of the crystal lattice, is detected in the region of the structural phase transitions. A symmetry analysis is carried out, and possible crystal structures of the low-temperature phase are indicated. Fiz. Tverd. Tela (St. Petersburg) 40, 2221–2225 (December 1998)     

Phase diagrams in an ultra-thin spin-1 transverse Ising film with bond or site dilution at surfaces

The phase diagrams of two nanoscaled thin films with bond and site dilutions at the surfaces, described by the spin-1 transverse Ising model, are investigated by the use of an effective field theory with correlations. A number of characteristic phenomena have been found in them, which are heavily dependent on the ratios (r = J₁/J and p = Ω_S/Ω, where J is the exchange interaction in the inner layer, J₁ is the exchange interaction between the surface and the next inner layer, Ω_S is the transverse field at the surfaces and Ω is the transverse field in the inner layer). Some of them have exhibited very similar behaviors found in the two spin-1/2 nanoscaled thin films with bond and site dilutions at the surfaces.     

Mixed spin- and spin- Ising models with random nearest-neighbour interactions

Using the effective field theory with correlations, we study mixed spin?3/2 and spin?1/2 Ising models with random bonds and crystal-field interactions on the honeycomb lattice. The nearest-neighbour couplings J_ij are taken as random variables with distribution P(J_ij) = pδ(J_ij ? J)+(1 ? p)δ(J_ij ? αJ), where J > 0 and |α| ≤ 1. In a certain range of negative values of α, the phase diagrams exhibit re-entrant behaviour. In detail, we investigate separately two kinds of disorder: Bond dilution (α = 0) and random ±J interactions (α = ?1). In both cases, the influence of the an-isotropy on the phase diagrams shows some new outstanding features.     

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     

Isomorphous phase transition and orientational freezing in hexagonal mixed crystal C 70(1 - x) C60x. A pseudospin model

A four-state pseudospin model is constructed for the isomorphous phase transition hcp-2↦hcp-1 in pure C₇₀ and in C₇₀-rich mixed crystal C _{70(1 - x)} C_60x. With the specific anisotropic pseudospin interactions adapted to the C₇₀ crystal the model is equivalent to a two-state Ising model in a temperature-dependent field. Replica symmetric state of the model is shown to approach the critical point when the width of distribution of random fields and/or of random bonds increases. The temperature of the phase transition and the phase equilibrium temperature then are practically constant, whereas the experiment shows their strong decrease with x. The main effect of dilution resides in an x-dependence of the model parameters. Dilatometric data on the hexagonal C _{70(1 - x)} C_60x are used to fit these parameters. A metastable disordered phase subsisting below the phase transition is discovered in a range of the model parameters and is shown to be responsible for the macroscopic behaviour of the system. A good agreement with experimental data is obtained for the spontaneous strain and for the x-dependence of the hysteresis. Received 20 April 2001 and Received in final form 26 September 2001     

Dynamic phase transitions and dynamic phase diagrams of the Blume–Emery–Griffiths model in an oscillating field: the effective-field theory based on the Glauber-type stochastic dynamics

Using the effective-field theory based on the Glauber-type stochastic dynamics (DEFT), we investigate dynamic phase transitions and dynamic phase diagrams of the Blume–Emery–Griffiths model under an oscillating magnetic field. We presented the dynamic phase diagrams in (T/J, h₀/J), (D/J, T/J) and (K/J, T/J) planes, where T, h₀, D, K and z are the temperature, magnetic field amplitude, crystal–field interaction, biquadratic interaction and the coordination number. The dynamic phase diagrams exhibit several ordered phases, coexistence phase regions and special critical points, as well as re-entrant behavior depending on interaction parameters. We also compare and discuss the results with the results of the same system within the mean-field theory based on the Glauber-type stochastic dynamics and find that some of the dynamic first-order phase lines and special dynamic critical points disappeared in the DEFT calculation.     

Effect of a pulsed magnetic field on the transverse resistance of a layered superconductor

The field dependences of the transverse resistance of a single crystal of the layered superconductor Bi₂Sr₂CaCu₂O_y (BSCCO-2212) with T _c 0≃92 K are studied in magnetic fields up to 50 T in the perpendicular orientation H⊥(ab). It is established that in the resistive region the resistance is a power-law function of the field, and the temperature dependence of the barrier height for flux creep is obtained. It is found that in a wide temperature range, 50–125 K, the transverse magnetoresistance of the crystal in the normal state and under conditions of superconductivity suppression by a strong magnetic field is negative and can be approximated by a linear law with a temperature-dependent slope. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 5, 420–425 (10 September 1998)     

Random field effects in field-driven quantum critical points

We investigate the role of disorder for field-driven quantum phase transitions of metallic antiferromagnets. For systems with sufficiently low symmetry, the combination of a uniform external field and non-magnetic impurities leads effectively to a random magnetic field which strongly modifies the behavior close to the critical point. Using perturbative renormalization group, we investigate in which regime of the phase diagram the disorder affects critical properties. In heavy fermion systems where even weak disorder can lead to strong fluctuations of the local Kondo temperature, the random field effects are especially pronounced. We study possible manifestation of random field effects in experiments and discuss in this light neutron scattering results for the field driven quantum phase transition in CeCu_5.8Au_0.2.     

A transverse electric current in triglycine sulphate ferroelectric crystal

The application of a prolonged transverse electric field at a temperature T_A < T_C leads to unexpected qualitative changes in dielectric and thermal properties of the uniaxial ferroelectric triglycine sulphate (TGS) crystal, where T_C is the critical temperature of the paraelectric-ferroelectric phase transition. The new properties can be still observed even after the transverse field has ceased to be applied as long as the temperature of the sample does not exceed T_A. However, annealing the sample above T_C leads to the restoration of the original state of the crystal. An electric current flowing along the direction perpendicular to the polar axis of the uniaxial TGS ferroelectric crystal was measured below the temperature T_A at which the prolonged transverse electric field had been formerly applied to the crystal for a few hours. The experimental data resemble the classic pyroelectric current flowing along the polar axis.     

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.