The Mixed Spin-1/2 and Spin-1 Ising–Heisenberg Model in the Mean-Field Approximation: a New Approach

Thermodynamic properties of the mixed spin-1 and spin-1/2 Ising–Heisenberg model are studied on a honeycomb lattice using a new approach in the mean-field approximation to analyze the effects of longitudinal D_z and transverse D_x crystal fields. The phase diagrams are calculated in detail by studying the thermal variations of the order parameters, i.e., magnetizations and quadrupole moments, and compared with the literature to assess the reliability of the new approach. It is found that the model yields both second-and first-order phase transitions, and tricritical points. The compensation behavior of the model is also investigated for the sublattice magnetizations, and longitudinal and transverse quadrupolar moments. The latter type of compensation is observed in the literature but its possible importance is overlooked.     

Phase diagrams in mixed spin-3/2 and spin-2 Ising system with two alternative layers within the effective-field theory

The phase diagrams in the mixed spin-3/2 and spin-2 Ising system with two alternative layers on a honeycomb lattice are investigated and discussed by the use of the effective-field theory with correlations. The interaction of the nearest-neighbour spins of each layer is taken to be positive (ferromagnetic interaction) and the interaction of the adjacent spins of the nearest-neighbour layers is considered to be either positive or negative (ferromagnetic or anti-ferromagnetic interaction). The temperature dependence of the layer magnetizations of the system is examined to characterize the nature (continuous or discontinuous) of the phase transitions and obtain the phase transition temperatures. The system exhibits both second-and first-order phase transitions besides triple point (T P ), critical end point (E), multicritical point (A), isolated critical point (C) and reentrant behaviour depending on the interaction parameters. We have also studied the temperature dependence of the total magnetization to find the compensation points, as well as to determine the type of behaviour, and N-type behaviour in N′eel classification nomenclature existing in the system. The phase diagrams are constructed in eight different planes and it is found that the system also presents the compensation phenomena depending on the sign of the bilinear exchange interactions.     

First-principles investigation of the electronic structure and magnetism of eskolaite

The electronic structure and magnetism of eskolaite are studied by using first-principles calculations where the on-site Coulomb interaction and the exchange interaction are taken into account and the LSDA+U method is used. The calculated energies of magnetic configurations are very well fitted by the Heisenberg Hamiltonian with interactions in five neighbour shells; interaction with two nearest neighbours is found to be dominant. The Néel temperature is calculated in the spin-3/2 pair-cluster approximation. It is found that the measurements are in good agreement with the calculations of lattice parameters, density of states, band gap, local magnetic moment, and the Néel temperature for the values of U and J that are close to those obtained within the constrained occupation method. The band gap is of the Mott--Hubbard type.     

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.     

Two-nucleon Excitation from p to sd Shell in 12,14C

The effect of the two-nucleon excitation from p to sd shell is discussed on 12C and 14C in the frame work of the nuclear shell model. The recently suggested shell-model Hamiltonian YSOX provides an suitable tool to investigate the 2 ~! excitation in psd region. Because the strength of the < pp|V |sdsd > interaction, which represents the interaction between the 0 and 2 ~! configurations, is considered in the construction of the Hamiltonian YSOX. The level of 12C is almost independent on the interaction, but excitation energies of certain states in 14C are strongly affected by it. Further investigation shows that the percentage of 2 ~! configuration in these states is quite different from that of the ground state. The non-linear effects of the < pp|V |sdsd > interaction on the configurations and transition rates are also discussed.     

Berry Phase of Composite System Induced by Time-Dependent Interaction

The Berry phase in a composite system induced by the time-dependent interaction is discussed. We choose two coupled spin-1/2 systems as the composite system： one of the subsystems is subjected to a static magnetic field, and the coupling parameters between two spins are controllable in time. We show that the time-dependent interaction can induce the Berry phase in a similar way as that a spin-1/2 system （qubit） is driven by an effective time-dependent magnetic field. Furthermore, using two consecutive cycles with opposite directions of both the static magnetic field as well as opposite signs of the coupling parameters, a nontrivial two-qubit unitary transformation purely based on Berry phases can be constructed.     

Energy of a Polaron in a Wurtzite Nitride Finite Parabolic Quantum Well

The effects of electron-phonon interaction on energy levels of a polaron in a wurtzite nitride finite parabolic quantum well （PQW） are studied by using a modified Lee-Low-Pines variational method. The ground state, first excited state, and transition energy of the polaron in the GaN/Al0.3Ga0.7N wurtzite PQW are calculated by taking account of the influence of confined LO（TO）-like phonon modes and the half-spaee LO（TO）-like phonon modes and considering the anisotropy of all kinds of phonon modes. The numerical results are given and discussed. The results show that the electron-phonon interaction strongly affects the energy levels of the polaron, and the contributions from phonons to the energy of a polaron in a wurtzite nitride PQW are greater than that in an A1GaAs PQW. This indicates that ehe electron-phonon interaction in a wurtzite nitride PQW is not negligible.     

Spin and valley filter in strain engineered silicene

The realization of a perfect spin or valley filtering effect in two-dimensional graphene-like materials is one of the fundamental objectives in spintronics and valleytronics. For this purpose, we study spin- and valley-dependent transport in a silicene system with spatially alternative strains. It is found that due to the valley-opposite gauge field induced by the strain, the strained silicene with a superlattice structure exhibits an angle-resolved valley and spin filtering effect when the spin–orbit interaction is considered. When the interaction that breaks the time reversal symmetry is introduced, such as the spin or valley dependent staggered magnetization, the system is shown to be a perfect spin and valley half metal in which only one spin and valley species is allowed to transport. Our findings are helpful to design both spintronic and valleytronic devices based on silicene.     

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.     

2D Pauli Equation with Hulthén Potential in the Presence of Aharonov-Bohm Effect

The 2D Pauli equation with Hulthén potential for spin-1/2 particle in the presence of Aharonov-Bohm (AB) field is solved analytically, on the assumption that an effective approximation is used for the centrifugal term.Singular and regular solutions of the problem are obtained. It is shown that the AB field lifts the degeneracy of the energy levels. The range of the flux parameter for which singular solutions are allowed is modified compared to the pure AB case. When the screening parameter vanishes, it is shown that the obtained energy spectrum becomes the same as that of the Aharonov-Bohm Coulomb problem.     

Study of Dynamics in Spin-1/2 Chain Using Adaptive Time-Dependent Density-Matrix Renormalization-Group Method

A numerical method of the adaptive time-dependent density-matrix renormalization-group (t-DMRG) is introduced to calculated one-dimensional quantum spin systems with next-nearest-neighbor interaction. The algorithm to study the local magnetization in spin-1/2 Heisenberg XX chain is checked. The analysis of error indicates that this method is efficient to study the spin-1/2 chain with next-nearest-neighbor interaction. By using of the method, the effects of the next-nearest-neighbor interaction on the dynamics of the local magnetization and entanglement entropy are studied.     

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.     

Magnetic properties of a mixed spin-1 and spin-2 Heisenberg ferrimagnetic system: Green’s function study

The magnetic behaviors of a mixed spin-1 and spin-2 Heisenberg ferrimagnetic system on a square lattice are studied by using the double-time temperature-dependent Green’s function technique. In order to decouple the higher order Green’s functions, Anderson and Callen’s decoupling and random phase approximations have been used. The system is described in the presence of an external magnetic field. We illustrate the influences of the nearest- and next-nearest-neighbor interactions and the single-ion anisotropies with an external magnetic field on compensation and critical temperatures. We found that the system that includes only the nearest-neighbor interaction and the single-ion anisotropies does not have a compensation temperature. When the next-nearest-neighbor interactions exceed a certain minimum value, a compensation temperature begins to appear. For some negative values of single-ion anisotropies, there exist first-order phase transitions. The system has first-order phase transition properties when it is under the influence of an external magnetic field.     

The Ferrimagnetic Mixed Spin-1/2 and Spin-1 Ising System on Layered Honeycomb Lattice

A mixed spin-1/2 and spin-1 Ising ferrimagnet with a layered honeycomb structure is studied within the framework of an effective-field theory with correlations. The effect of interlayer interactions and a single-ion anisotropy on the existence of the compensation temperature and tricritical point is investigated. In particular, it is pointed out that the tricritical point may be only possible if interlayer interactions are nonzero.     

Green's function study of a mixed spin-1 and spin-3/2 Heisenberg ferrimagnetic system

The magnetic properties of a mixed spin-1 and spin-3/2 Heisenberg ferrimagnetic system on a square lattice are investigated by using the double-time temperature-dependent Green's function technique. In order to decouple the higher order Green's functions, Anderson and Callen's decoupling and random phase approximations have been used. The nearest- and next-nearest-neighbor interactions and the single-ion anisotropies are considered and their effects on compensation and critical temperature are studied.     

Mean-Field Studies of a Mixed Spin-3/2 and Spin-2 and a Mixed Spin-3/2 and Spin-5/2 Ising System with Different Anisotropies

The magnetic properties of a mixed spin-3/2 and spin-2 and a mixed spin-3/2and spin-5/2 Ising ferromagnetic system with different anisotropies are studied by means of mean-field theory (MFT). The dependence of the phase diagram on single-ion anisotropy strengths is studied too. In the mixed spin-3/2 and spin-2 Ising model, besides the second-order phase transition, the first order-disorder phase transition and the tricritical line are found. In the mixed spin-3/2 and spin-5/2 Ising model, there is no first-order transition and tricritical line.     

Spin-1/2 singleton dipole in three dimensions

The Lagrangian and Hamiltonian formulations for the three-dimensional spin-1/2 singleton dipole theory are obtained. It is found that the dynamics is determined solely by some precise boundary conditions at spatial infinity of anti-de Sitter spacetime. In particular, the Hamiltonian reduces to an integral over a one-dimensional boundary surface.     

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.

     

Spin-3/2 fields in flat space-time

The equations for the spin-3/2 (Rarita-Schwinger) field given by linearized simple supergravity are written in space-plus-time form in terms ofSU(2) spinors, assuming that the background space-time is flat. Some consequences of these equations are analyzed and a Hamiltonian structure for the Rarita-Schwinger field is obtained.