Critical and Compensation Temperatures of the Ising Bilayer System Consisting of Spin-1/2 and Spin-1 Atoms

The critical and compensation temperatures of the bilayer Bethe lattices with one of the layers having only spin-1/2 atoms and the other having only spin-1 atoms placed symmetrically are studied by using exact recursion relations in a pairwise approach. The Hamiltonian of the model consist of the bilinear intralayer coupling constants of the two layers J ₁ and J ₂ for the interactions of the atoms in layers with spin-1/2 and spin-1, respectively, and the bilinear interlayer coupling constant J ₃ between the adjacent atoms with spin-1/2 and spin-1 of the layers. After obtaining the ground state phase diagram with J ₁ > 0, the variations of the order-parameters and the free energy are investigated to obtain the phase diagram of the model by considering only the ferromagnetic ordering of the layers, i.e. J ₁ > 0 and J ₂ > 0, and ferromagnetic or antiferromagnetic ordering of the adjacent spins of the layers, J ₃ > 0 or J ₃ < 0, respectively. It was found that the system presents both second- and first-order phase transitions and, tricritical points. The compensation temperatures was also observed for the appropriate values of the system parameters. PACS: 05.50.+q 05.70.Fh 64.60.Cn 75.10.Hk     

Renormalization Group Study of the Mixed Spin-1 and Spin-3/2 Blume-Emery-Griffiths Model with Attractive Biquadratic Coupling

The mixed spin-1 and spin-3/2 Blume-Emery-Griffiths model with attractive biquadratic coupling is investigated in the framework of the Migdal-Kadanoff Renormalization Group method. By changing the ratio R > 0 of biquadratic and bilinear exchange interactions and according to the different values of crystal field interactions, we have determined six main types of phase diagrams. The full flow in the parameters space of the Hamiltonian was established and the fixed points obtained are drawn up in a table. In addition, we have determined the eigenvalues of the transformation of the group in the vicinity of the critical points. Finally, the introduction of a positive biquadratic interaction was discussed.

     

Dynamic Dipole and Quadrupole Phase Transitions in the Kinetic Spin-3/2 Model

The dynamic phase transition has been studied, within a mean-field approach, in the kinetic spin-3/2 Ising model Hamiltonian with arbitrary bilinear and biquadratic pair interactions in the presence of a time dependent oscillating magnetic field by using the Glauber-type stochastic dynamics. The nature (first- or second-order) of the transition is characterized by investigating the behavior of the thermal variation of the dynamic order parameters and as well as by using the Liapunov exponents. The dynamic phase transitions (DPTs) are obtained and the phase diagrams are constructed in the temperature and magnetic field amplitude plane and found nine fundamental types of phase diagrams. Phase diagrams exhibit one, two or three dynamic tricritical points, and besides a disordered (D) and the ferromagnetic-3/2 (F_3/2) phases, six coexistence phase regions, namely F _3/2+ F _1/2, F _3/2+ D, F _3/2+ F _1/2+ FQ, F _3/2+ FQ, F _3/2+ FQ + D and FQ + D, exist in which depending on the biquadratic interaction. PACS number(s): 05.50.+q, 05.70.Fh, 64.60.Ht, 75.10.Hk     

The temperature-dependent phase diagrams of the spin-3/2 Ising model on a FM/AFM two-layer lattice with a crystal field

The temperature-dependent phase diagrams of the spin-3/2 Ising model on a two-layer Bethe lattice with ferromagnetic (FM)/antiferromagnetic (AFM) intra-layer and either FM or AFM type inter-layer interactions are investigated under a constant magnetic field (H) and in the presence of a crystal field (D) by using exact recursion equations in a pairwise approach for coordination numbers q=3,4 and 6, in detail. In the light of the ground-state (GS) phase diagrams, the temperature-dependent phase diagrams of the model are obtained by studying the thermal variations of the order parameters, response functions and free energy. Then, they are illustrated on the (kT/J₁,J₃/J₁) and (kT/J₁,J₂/J₁) planes for the given system parameters. It is observed that the system exhibits first- and second-order phase transitions for all q values, and hence, in some cases, tricritical points. The existence of critical-end points and that of isolated points are also observed. The re-entrant behavior owes its presence to the two Néel temperatures, T_N, that are present for all q.     

The mixed-spin ternary-alloy in the form of ABpC1−p on the Bethe lattice

The AB_pC_1−p type of mixed ferromagnetic-ferrimagnetic ternary-alloy with A (spin-3/2), B (spin-1) and C (spin-5/2) ions was studied on the Bethe lattice with the odd numbered shells containing only A ions, while the even numbered shells either containing B or C ions randomly. The phase diagrams were obtained on the (R=|J_AC|/J_AB,kT_c/J_AB) and (p, kT_c/J_AB) planes for given values of p and R, respectively, with the coordination numbers z=3, 4, 5 and 6. The explicit dependence of the phase diagrams on z and each shell of the Bethe lattice having only one type of ion lead to some differences when compared with the previous works. The model presents one or two compensation temperatures for appropriate values of the system parameters.     

Dynamic Phase Transitions and Compensation Temperatures in a Mixed Spin-3/2 and Spin-5/2 Ising System

We examine the dynamic phase transitions and the dynamic compensation temperatures, within a mean-field approach, in the mixed spin-3/2 and spin-5/2 Ising system with a crystal-field interaction under a time-varying magnetic field on a hexagonal lattice by using Glauber-type stochastic dynamics. The model system consists of two interpenetrating sublattices with σ=3/2 and S=5/2. The Hamiltonian model includes intersublattice, intrasublattice, and crystal-field interactions. The intersublattice interaction is considered antiferromagnetic and to be a simple but interesting model of a ferrimagnetic system. We employ the Glauber transition rates to construct the mean-field dynamic equations, and we solve these equations in order to find the phases in the system. We also investigate the thermal behavior of the dynamic sublattice magnetizations and the dynamic total magnetization to obtain the dynamic phase transition points and compensation temperatures as well as to characterize the nature (continuous and discontinuous) of transitions. We also calculate the dynamic phase diagrams including the compensation temperatures in five different planes. According to the values of Hamiltonian parameters, five different fundamental phases, three different mixed phases, and six different types of compensation behaviors in the Néel classification nomenclature exist in the system.     

The effective-field theory studies of critical phenomena in a mixed spin-1 and spin-2 Ising model on honeycomb and square lattices

An effective-field theory with correlations has been used to study critical behaviors of a mixed spin-1 and spin-2 Ising system on a honeycomb and square lattices in the absence and presence of a longitudinal magnetic field. The ground-state phase diagram of the model is obtained in the longitudinal magnetic field (h) and a single-ion potential or crystal-field interaction (Δ) plane. The thermal behavior of the sublattice magnetizations of the system are investigated to characterize the nature of (continuous and discontinuous) of the phase transitions and obtain the phase transition temperature. The phase diagrams are presented in the (Δ/|J|, k_BT/|J|) plane. The susceptibility, internal energy and specific heat of the system are numerically examined and some interesting phenomena in these quantities are found due to the absence and presence of the applied longitudinal magnetic field. Moreover, the system undergoes second- and first-order phase transition; hence, the system gives a tricritical point. The system also exhibits reentrant behavior.     

Magnetic properties of an anti-ferromagnetic and ferrimagnetic mixed spin-1/2 and spin-5/2 Ising model in the longitudinal magnetic field within the effective-field approximation

The magnetic properties of an anti-ferromagnetic and ferrimagnetic mixed spin-1/2 and spin-5/2 Ising model with a crystal field in a longitudinal magnetic field on the honeycomb (z=3) and square lattice (z=4) are studied by using the effective-field theory with correlations. The ground state phase diagram of the model is obtained in the longitudinal magnetic field (h) and a single-ion potential or crystal-field interaction (Δ) plane. We also investigate the thermal variations of the sublattice and total magnetizations, and present the phase diagrams in the (Δ/|J|, ) plane. The phase diagrams have one, two or even three compensation temperatures depending on the values of the crystal-field interaction. Moreover, the susceptibility, internal energy and specific heat of the system are numerically examined, and some interesting phenomena in these quantities are found due to the applied longitudinal magnetic field.     

The effect of the heating rate on the phase transition

ABSTRACT

The simple cubic spin-1 Ising model exhibits the ferromagnetic (F)–ferromagnetic (F) phase transition in the low temperature region for the interval 1.40 < d = D/J < 1.48 at k = K/J = –0.5. The degree of the F-F phase transition determines the special point on the (k_BT/J, d) phase diagram. In this paper, the critical behavior of the F-F phase transition was investigated for different heating rates using the cellular automaton heating algorithm. The universality class and the type of F-F phase transition were analyzed using the finite-size scaling theory and the power law relations. The results show that the F-F phase transition may be the second order, the first order or the weak first order depending on the heating rate in the interval 1.40 < d < 1.48 for k = –0.5.     

Spin-3/2 Ising model AFM/AFM two-layer lattice with crystal field

The spin-3/2 Ising model is investigated for the case of antiferromagnetic (AFM/AFM) interactions on the two-layer Bethe lattice by using the exact recursion relations in the pairwise approach for given coordination numbers q=3, 4 and 6 when the layers are under the influences of equal external magnetic and equal crystal fields. The ground state (GS) phase diagrams are obtained on the different planes in detail and then the temperature-dependent phase diagrams of the system are calculated accordingly. It is observed that the system presents both second- and first-order phase transitions for all q, therefore, tricritical points. It is also found that the system exhibits double-critical end points and isolated points. The model also presents two Néel temperatures, T_N, and the existence of which leads to the reentrant behaviour.     

Critical properties of mixed spin-1 and spin-5/2 with equal and unequal crystal fields

The effects of assuming equal or unequal crystal fields (CF) on the phase diagrams of a mixed spin-1 and spin-5/2 system are investigated in terms of the recursion relations on the Bethe lattice (BL). The equal CF case was considered for the coordination numbers q=3, 4, and 6, while for q=3 the unequal CF case was also studied. It was found that for the equal CF case, the model exhibits second-order phase transitions and two compensation temperatures for all q, the reentrant behavior for q=4 and first-order phase transitions and tricritical point (TCP) for q=6. In the unequal CF case for q=3, the system yields first- and second-order phase transitions, TCP's, and three compensation temperatures. In addition, the TCP's in a very short range are classified as the stable and unstable ones depending on their free energies.     

Exact results of an alternating-bond mixed spin-1/2 and spin-1 Ising chain with both longitudinal and transverse single-ion anisotropies

The alternating-bond mixed spin-1/2 and spin-1 Ising chain with both longitudinal and transverse single-ion anisotropies are solved exactly by means of a mapping of the spin-1/2 transverse Ising chain and the Jordan-Wigner transformation. The ground state quantities are strongly dependent on the model Hamiltonian parameters J₁, J₂, D_x and D_z. We obtain the quasi-particles' spectra Λ_k, the dimerization gap Δ_d, the minimal energy Δ₀ for exciting a fermion quasi-particle, the minimal energy gap Δ_h for exciting a hole and the ground state energy E_g. The phase diagram of the ground state is also given. The results show that the alternating bond just quantitatively changes the ground state properties; no matter the nearest-neighbor exchange interactions J₁ and J₂ are equal or not, when D_z≥0 for any finite value of D_x, there is no quantum critical point and the ground state is always in a spin ordered phase.     

Spin-1/2 equation with indefinite metric

We study a Schrödinger equation involving a Hamiltonian that is a second-order differential operator, describes free spin-1/2 particles with both energy signs and a definite mass, and depends on a parameterG. One obtains the usual Dirac Hamiltonian by settingG=±i, but for real values ofG the one-particle theory developed here possesses an indefinite metric, so negative energy states have negative normalization. Although the new equation is not manifestly covariant, it is demonstrated that it can be made invariant under proper orthochronous Poincaré transformations; it is also invariant under the CPT transformation and charge conjugation, but not, as we interpret it, under space inversion.Supported in part by the U.S. Energy Research and Development Administration.     

Effects of the Quenched Random Crystal Field on the Dynamic Spin-1 Blume-Capel Model

In this study, we have analyzed the dynamical phase transitions of spin-1 Blume-Capel model with quenched random crystal field under the effect of a time dependent oscillating magnetic field. We have obtained the magnetic field, temperature (h,T) cross sections of the global phase diagram for constant values of the concentration and the amplitude of the single-ion anisotropy within mean field approximation. There are regions of the phase space where both ordered and disordered phases coexist. In addition, the dynamic phase transition from one regime to the other can be a first- or a second-order depending on the region in the phase diagram. Hence, the system exhibits a number of interesting phenomena and a rich variety of phase diagrams with type being according to the concentration p of active local crystal fields.     

An exact formulation of the Blume-Emery-Griffiths model on a two-fold Cayley tree model

A two-fold Cayley tree graph with fully q-coordinated sites is constructed and the spin-1 Ising Blume-Emery-Griffiths model on the constructed graph is solved exactly using the exact recursion equations for the coordination number q = 3. The exact phase diagrams in (kT/J, K/J ) and (kT/J, D/J) planes are obtained for various values of constants D/J and K/J, respectively, and the tricritical behavior is found. It is observed that when the negative biquadratic exchange (K) and the positive crystal-field (D) interactions are large enough, the tricritical point disappears in the (kT/J, K/J) plane. On the other hand, the system always exhibits a tricritical behavior in the phase diagram of (kT/J, D/J) plane. Received 8 June 2001 and Received in final form 28 September 2001     

Quantum and Classical Thermal Correlations in the XXZ Spin-1/2 Chain

We compute the quantum dissonance Q (non-entangled quantum correlation), entanglement E, quantum discord D (total quantum correlation) and classical correlation C in the eight-qubit XXZ spin-1/2 chain at finite temperatures. We find that not only D but also Q and C can clearly detect the critical points associated to quantum phase transitions for this model at finite temperatures. Moreover, Q can detect the special points of the system where the entanglement just appears or completely vanishes. Finally, we obtain two simple dominance relations: C≥E and D≥E+Q. Except these there are no other simple ordering relations in this model.     

Spin-1/2 Ising model on a AFM/FM two-layer Bethe lattice in a staggered magnetic field

A bilayer spin-1/2 Ising model consisting of two superposed Bethe lattices with antiferromagnetic/ferromagnetic interactions is studied by the use of exact recursion relations in a pairwise approach in the presence of an external staggered magnetic field. Besides the ground state phase diagrams calculated in different possible planes of the model parameters space, the thermal variations of the order-parameters and the free energy are investigated to obtain the temperature-dependent phase diagrams of the model for different values of the coordination numbers q. Our calculations reveal that depending on the strength of the model parameters, the model exhibits a variety of interesting phase transitions and therefore phase diagrams.     

Spin-0 and spin-1/2 particles in a constant scalar-curvature background

We study the Klein-Gordon and Dirac equations in the presence of a background metric ds²=−dt²+dx²+e^−2gx(dy²+dz²) in a semi-infinite lab (x>0). This metric has a constant scalar-curvature R=6g² and is produced by a perfect fluid with equation of state p=−ρ/3. The eigenfunctions of spin-0 and spin-1/2 particles are obtained exactly, and the quantized energy eigenvalues are compared. It is shown that both of these particles must have nonzero transverse momentum in this background. We show that there is a minimum energy E²_min=m²c⁴+g²c²?² for bosons (E_KG>E_min), while the fermions have no specific ground state (E_Dirac>mc²).     

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.     

Hexagonal Type Ising Nanowire with Spin-1 Core and Spin-2 Shell Structure

Thermodynamic properties and phase diagrams of a mixed spin-(1,2) Ising ferrimagnetic system with single ion anisotropy on hexagonal nanowire are studied by using effective-field theory with correlations. The susceptibility, internal energy and specific heat of the system are numerically examined and some interesting phenomena in these quantities are found. The effect of the Hamiltonian parameters on phase diagrams are examined in detail. Besides second-order phase transition, lines of first-order transition and tricritical points are found. In particular, we found that for some negative values of single-ion anisotropies, there exist first-order phase transitions.