Phase diagrams of spin-3/2 Ising model in the presence of random crystal field within the effective field theory based on two approximations

The bimodal random crystal field （A） effects are investigated on the phase diagrams of spin-3/2 Ising model by using the effective-field theory with correlations based on two approximations： the general van der Waerden identity and the approximated van der Waerden identity. In our approach, the crystal field is either turned on or turned off randomly for a given probability p or q = 1 -p, respectively. Then the phase diagrams are constructed on the （A,kT/J） and （p,kT/J） planes for given p and A, respectively, when the coordination number is z = 3. Furthermore, the effect of randomization of the crystal field is illustrated on the （△,kT/J） plane for p = 0.5 when z - 3,4, and 6. All these are carried out for both approximations and then the results are compared to point out the differences. In addition to the lines of second-order phase transitions, the model also exhibits first-order phase transitions and the lines of which terminate at the isolated critical points for high p values.     

Bond Dilution Effects on Bethe Lattice the Spin-1 Blume–Capel Model

The bond dilution effects are investigated for the spin-1 Blume–Capel model on the Bethe lattice by using the exact recursion relations. The bilinear interaction parameter is either turned on ferromagnetically with probability p or turned off with probability 1-p between the nearest-neighbor spins. The thermal variations of the order-parameters are studied in detail to obtain the phase diagrams on the possible planes spanned by the temperature(T), probability(p) and crystal field(D) for the coordination numbers q = 3, 4, and 6. The lines of the second-order phase transitions,T_c-lines, combined with the first-order ones, T_t-lines, at the tricritical points(TCP) are always found for any p and q on the(T, D)-planes. It is also found that the model gives only T_c-lines, Tc-lines combined with the T_t-lines at the TCP's and only Tt-lines with the consecutively decreasing values of D on the(T, p)-planes for all q.     

Spin-1 Blume-Capel model with longitudinal random crystal and transverse magnetic fields：A mean-field approach

The spin-1 Blume-Capel model with transverse and longitudinal external magnetic fields h, in addition to a longitudinal random crystal field D, is studied in the mean-field approximation. It is assumed that the crystal field is either turned on with probability p or turned off with probability 1 p on the sites of a square lattice. Phase diagrams are then calculated on the reduced temperature crystal field planes for given values of γ=Ω/J and p at zero h. Thus, the effect of changing γ and p are illustrated on the phase diagrams in great detail and interesting results are observed.     

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.     

Phase diagrams of the spin-2 Ising model in the presence of a quenched diluted crystal field distribution

We have investigated the random crystal field effects on the phase diagrams of the spin-2 Blume-Capel model for a honeycomb lattice using the effective-field theory with correlations.To do so,the thermal variations of magnetization are studied via calculating the phase diagrams of the model.We have found that the model displays both second-order and first-order phase transitions in addition to the tricritical and isolated points.Reentrant behavior is also observed for some appropriate values of certain system parameters.Besides the usual ground-state phases of the spin-2 model including ±2,±1,and 0,we have also observed the phases ±3/2 and ±1/2,which are unusual for the spin-2 case.     

Phase Diagram of Transverse Spin-2 Ising Model with Longitudinal Crystal Field

The transverse spin-2 Ising ferromagnetic model with a longitudinal crystal field is studied within the mean-field theory. The phase diagrams and magnetization curves are obtained by diagonalizing the Hamiltonian Hi of the Ising system numerically, and the first order-order phase transitions, the first order-disorder phase transitions, and the second-order phase transitions are discussed in details. Reentrant phenomena occur when the value of the transverse field is not zero and the reentrant diagram is given.     

Glassy behaviour of random field Ising spins on Bethe lattice in external magnetic field

The thermodynamics and the phase diagram of random field Ising model (RFIM) on Bethe lattice are studied by using a replica trick. This lattice is placed in an external magnetic field (B). A Gaussian distribution of random field (hi) with zero mean and variance hi2 = HR2F is considered. The free-energy (F ), the magnetization (M) and the order parameter (q) are investigated for several values of coordination number (z). The phase diagram shows several interesting behaviours and presents tricritical point at critical temperature TC = J/k and when HRF = 0 for finite z. The free-energy (F) values increase as T increases for different intensities of random field (HRF) and finite z. The internal energy (U) has a similar behaviour to that obtained from the Monte Carlo simulations. The ground state of magnetization decreases as the intensity of random field HRF increases. The ferromagnetic (FM)-paramagnetic (PM) phase boundary is clearly observed only when z →∞. While FM-PM-spin glass (SG) phase boundaries are present for finite z. The magnetic susceptibility (χ) shows a sharp cusp at TC in a small random field for finite z and rounded different peaks on increasing HRF.     

Monte Carlo study of nanowire magnetic properties

In this work, we use Monte Carlo simulations to study the magnetic properties of a nanowire system based on a honeycomb lattice, in the absence as well as in the presence of both an external magnetic field and crystal field. The system is formed with NL layers having spins that can take the values σ = ±1/2 and S = ±1, 0. The blocking temperature is deduced, for each spin configuration, depending on the crystal field Δ. The effect of the exchange interaction coupling Jp between the spin configurations σ and S is studied for different values of temperature at fixed crystal field. The established ground-state phase diagram, in the plane (Jp ,Δ), shows that the only stable configurations are: (1/2, 0), (1/2, +1), and (1/2,-1). The thermal magnetization and susceptibility are investigated for the two spin configurations, in the absence as well as in the presence of a crystal field. Finally, we establish the hysteresis cycle for different temperature values, showing that there is almost no remaining magnetization in the absence of the external magnetic field, and that the studied system exhibits a super-paramagnetic behavior.     

Nonchaotic random behaviour in the second order autonomous system

Evidence is presented for the nonchaotic random behaviour in a second-order autonomous deterministic system. This behaviour is different from chaos and strange nonchaotic attractor. The nonchaotic random behaviour is very sensitive to the initial conditions. Slight difference of the initial conditions will generate wholly different phase trajectories. This random behaviour has a transient random nature and is very similar to the coin-throwing case in the classical theory of probability. The existence of the nonchaotic random behaviour not only can be derived from the theoretical analysis, but also is proved by the results of the simulated experiments in this paper.     

Non-Maximal Tripartite Entanglement Degradation of Dirac and Scalar Fields in Non-Inertial Frames

The π-tangle is used to study the behavior of entanglement of a nonmaximal tripartite state of both Dirac and scMar fields in accelerated frame. For Dirac fields, the degree of degradation with acceleration of both one-tangle of accelerated observer and π-tangle, for the same initial entanglement, is different by just interchanging the values of probability amplitudes. A fraction of both one-tangles and the π-tangle always survives for any choice of acceleration and the degree of initial entanglement. For scalar field, the one-tangle of accelerated observer depends on the choice of values of probability amplitudes and it vanishes in the range of infinite acceleration, whereas for 1r-tangle this is not always true. The dependence of π-tangle on probability amplitudes varies with acceleration. In the lower range of acceleration, its behavior changes by switching between the values of probability amplitudes and for larger values of acceleration this dependence on probability amplitudes vanishes. Interestingly, unlike bipartite entanglement, the degradation of π-tangle against acceleration in the case of sca/ar fields is slower than for Dirac fields.     

双模随机晶场对纳米管上Blume-Capel模型磁化强度和相变的影响

近年来, 磁性纳米管的物理性质和相关应用得到了人们的广泛关注. 利用有效场理论研究了纳米管上双模随机晶场中Blume-Capel模型的磁化强度和相变性质, 得到了系统的磁化强度与温度和随机晶场的关系及其相图. 结果表明: 系统在稀释晶场、交错晶场和同向晶场中会表现出不同的磁学性质和相变行为; 稀释晶场和交错晶场会抑制系统的磁化强度, 导致其基态饱和值小于1, 而同向晶场则不会; 随着随机晶场参量的变化, 系统存在多个相变温度, 并呈现出三临界现象和重入现象.     

双模随机交错晶场中最近邻弱交换相互作用对重入现象的影响

利用有效场理论研究了双模随机交错晶场中混合自旋 Blume-Capel 模型纳米管系统的重入现象, 发现了系统的重入现象与晶场取值概率、 晶场强度和外壳层与内壳层格点间最近邻交换相互作用的关系. 结果表明: 取值概率、 交换相互作用、 晶场强度和温度等诸多因素相互竞争, 使系统表现出丰富的磁化现象: 正( 负) 晶场较弱时, 系统只发生二级相变; 随着正( 负) 晶场增强, 系统的二级相变消失, 呈现一级相变; 一定条件下, 系统会出现重入现象.     

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.     

外壳层最近邻交换相互作用对Blume-Capel模型相变行为的影响

利用有效场理论研究了纳米管上双模随机晶场中混合自旋Blume-Capel模型的相变行为。结果表明，系统相变行为与取值概率、晶场强度比值、晶场参数、温度以及外壳层最近邻交换相互作用密切相关。取值概率、晶场强度比值、晶场参数和外壳层最近邻交换相互作用等诸多因素相互竞争，影响系统的一级和二级相变以及临界点。     

Random crystal field effects for spin-3/2 Blume-Capel model

The effects of crystal field (Δ) which is randomly turned on with probability p or turned off with probability 1−p on the sites of the Bethe lattice are investigated to study the critical behavior of the spin-3/2 Blume-Capel model. The order-parameters are obtained in terms of the recursion relations and then the possible phase diagrams are calculated at finite temperatures for given system parameters p, Δ and coordination numbers z=3, 4, 5 and 6. It was found that the phase diagrams change drastically for given probability and randomness. The first-order phase transitions are only found for higher p values and the lines of which get shorter and eventually disappear as p decreases. The critical lines do not present any qualitative differences with z, but they are seen at higher temperatures for higher z.     

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.     

Random-bond and random-anisotropy effects in the phase diagram of the Blume–Capel model

We report on Monte Carlo studies of the influence of quenched randomness on the phase diagram of the three-dimensional (3D) Blume–Capel model. The randomness is supposed to act either on the exchange coupling constants (bond randomness) or on the anisotropy distribution. With increasing disorder, first-order phase transitions are shown to change into second-order phase transitions. The trajectory of the tricritical point in the phase space as a function of disorder is presented. We have also calculated critical exponents at some points in the second-order phase region which show a change of universality class in agreement with the Harris criterion.     

The random-field Ising model with asymmetric bimodal probability distribution

The Ising model, in the presence of a random field, is investigated within the mean-field approximation based on Landau expansion. The random field is drawn from the bimodal probability distribution P(h)=pδ(h−h₀)+(1−p)δ(h+h₀), where the probability p assumes any value within the interval [0,1], asymmetric distribution. The prevailing transitions are of second-order but, for some values of p and h₀, first-order phase transitions take place for smaller temperatures and higher h₀, thus confirming the existence of a tricritical point. Also, the possible reentrant phenomena in the phase diagram (T−h₀ plane) occur for appropriate values of p and h₀. Using the variational principle, we determine the equilibrium equation for magnetization and solve it for both transitions and at the tricritical point in order to determine the magnetization profile with respect to h₀.     

Uncovering the secrets of the 2D random-bond Blume-Capel model

The effects of bond randomness on the ground-state structure, phase diagram and critical behavior of the square lattice ferromagnetic Blume-Capel (BC) model are discussed. The calculation of ground states at strong disorder and large values of the crystal field is carried out by mapping the system onto a network and we search for a minimum cut by a maximum flow method. At finite temperatures the system is studied by an efficient two-stage Wang-Landau (WL) method for several values of the crystal field, including both the first- and second-order phase transition regimes of the pure model. We attempt to explain the enhancement of ferromagnetic order and we discuss the critical behavior of the random-bond model. Our results provide evidence for a strong violation of universality along the second-order phase transition line of the random-bond version.