Temperature fluctuations for a finite system of classical spin-1/2 particles

For sufficiently large but finite N independent spin-1/2 paramagnets in a constant magnetic field, the orientation of every spin has the same probability to be parallel or anti-parallel to that of the magnetic field. In our statistical ensemble treatment, all fundamental thermodynamic quantities fluctuate, including the entropy and temperature, and all fluctuations are gradually vanishing as the temperature itself approaches zero. Our approach presents a remedy of infinite temperature fluctuations and reproduces other reasonable results that are given by standard theory.     

Resolution of the Klein paradox for spin-1/2 particles

The problem of a relativistic spin-1/2 particle scattering from a step potential is solved within the theoretical framework of relativistic dynamics. This treatment avoids the Klein paradox. An experiment for testing the theory is suggested.     

Berry phase for spin-1/2 particles moving in a space-time with torsion

Berry phase for a spin-1/2 particle moving in a flat space-time with torsion is investigated in the context of the Einstein–Cartan–Dirac model. It is shown that if the torsion is due to a dense polarized background, then there is a Berry phase only if the fermion is massless and its momentum is perpendicular to the direction of the background polarization. The order of magnitude of this Berry phase is discussed in other theoretical frameworks. Received: 12 February 2001 / Revised version: 2 May 2001 / Published online: 29 June 2001     

Random crystal-field effects in a mixed spin-1/2 and spin-2 ferrimagnetic Ising system

The magnetic properties of a mixed spin ferrimagnetic system σ?=?1/2 and S?=?2 at the sites of a square lattice with a random crystal field are studied by the mean field approximation. The ground state of the system is determined and the total magnetization is plotted according to the model parameters. Different behaviors for the thermal dependence of the magnetization are highlighted. In particular, one sees the appearance of one or two compensating points and many types of phase diagrams with first and second order phase transition lines as well as isolated critical and tricritical points.     

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).     

Dirac-kahler equation and calculation of matrix elements for spin-1/2 particles

An explicit tensor method presented for calculating the matrix elements of the interaction of massive spin-1/2 particles does not involve calculation of traces from the products of Dirac matrices.Belorussian State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 39–42, October, 1994.     

Mixed spin-1 and spin-3/2 Ising system with two alternative layers of a honeycomb lattice within the effective-field theory

An effective-field theory with correlations is developed for a mixed spin-1 and spin-3/2 Ising system with two alternative layers of a honeycomb lattice. Spin-1 atoms and spin-3/2 atoms are distributed in alternative layers of a honeycomb lattice. We consider that the nearest-neighbor spins of each layer are coupled ferromagnetically and the interaction between the vertically aligned spins and adjacent spins are coupled either ferromagnetically or antiferromagnetically depending on the sign of the bilinear exchange interactions. We investigate the temperature dependence of the total magnetization to find the compensation points and to determine the type of compensation behavior. We present the phase diagrams in different planes for h=0, and the phase diagrams contain the paramagnetic, nonmagnetic and ferrimagnetic phases. The system also presents a tricritical behavior besides multicritical point (A), isolated critical point (C) and double critical end point (B) depending on the interaction parameters.     

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.     

The possibility of two compensation points in a ferrimagnetic mixed spin-1 and spin-3/2 Ising system using Bethe lattice approach

We give an exact formulation of a mixed spin-1 and spin-3/2 Ising model on the Bethe lattice, which shows ferrimagnetism and compensation points. The model incorporates antiferromagnetic nearest-neighbor interaction which is relevant to describe ferrimagnetism. The influence of two sublattice crystal fields, D_A and D_B, on compensation points is studied in detail. For certain crystal-field values, the single or double compensation temperature may occur in the present system.     

Dependence on dilution of critical and compensation temperatures of a two-dimensional mixed spin-1/2 and spin-1 system

In this study, dependence on site dilution of critical and compensation temperatures of a two-dimensional mixed spin-1/2 and spin-1 system has been investigated with Monte Carlo simulation. The dependence of the thermal and magnetic behaviors on dilution of mixed spin system has been discussed. We have shown that the critical and compensation temperatures of diluted mixed spin system linearly decrease with increasing number of diluted sites.     

Kinetics of a mixed spin-1/2 and spin-3/2 Ising ferrimagnetic model

We present a study, within a mean-field approach, of the kinetics of a mixed ferrimagnetic model on a square lattice in which two interpenetrating square sublattices have spins that can take two values, , alternated with spins that can take the four values, . We use the Glauber-type stochastic dynamics to describe the time evolution of the system with a crystal-field interaction in the presence of a time-dependent oscillating external magnetic field. The nature (continuous and discontinuous) of transition is characterized by studying the thermal behaviors of average order parameters in a period. The dynamic phase transition points are obtained and the phase diagrams are presented in the reduced magnetic field amplitude (h) and reduced temperature (T) plane, and in the reduced temperature and interaction parameter planes, namely in the (h, T) and (d, T) planes, d is the reduced crystal-field interaction. The phase diagrams always exhibit a tricritical point in (h, T) plane, but do not exhibit in the (d, T) plane for low values of h. The dynamic multicritical point or dynamic critical end point exist in the (d, T) plane for low values of h. Moreover, phase diagrams contain paramagnetic (p), ferromagnetic (f), ferrimagnetic (i) phases, two coexistence or mixed phase regions, (f+p) and (i+p), that strongly depend on interaction parameters.     

Magnetic properties of a random diluted spin-1/2, 1, 3/2 superlattice

Using the effective-field theory we studied the magnetic properties of a random diluted spin-1/2, 1, 3/2 superlattice which consists of three different ferromagnetic materials. The critical temperature of the system is studied as a function of the concentration of magnetic atoms and exchange interactions in each layer. The temperature dependence of magnetization shows that the properties of the diluted system are different from those of the corresponding pure system.     

Geometric phase for degenerate states of spin-1 and spin-1/2 pair

The geometric phase of a bi-particle model is discussed. One can drive the system to evolve by applying an external magnetic field, thereby controlling the geometric phase. The model has degenerate lowest-energy eigenvectors. The initial state is assumed to be the linear superposition or mixture of the eigenvectors. The relationship between the geometric phase and the structures of the initial state is considered, and the results are extended to a more general model.      

Phase diagrams of a nonequilibrium mixed spin-1/2 and spin-2 Ising ferrimagnetic system under a time-dependent oscillating magnetic field

We present phase diagrams for a nonequilibrium mixed spin-1/2 and spin-2 Ising ferrimagnetic system on a square lattice in the presence of a time dependent oscillating external magnetic field. We employ the Glauber transition rates to construct the mean-field dynamical equations. The time variation of the average magnetizations and the thermal behavior of the dynamic magnetizations are investigated, extensively. The nature (continuous or discontinuous) of the transitions is characterized by studying the thermal behaviors of the dynamic magnetizations. The dynamic phase transition points are obtained and the phase diagrams are presented in two different planes. Phase diagrams contain paramagnetic (p) and ferrimagnetic (i) phases, and one coexistence or mixed phase region, namely the i+p, that strongly depend on interaction parameters. The system exhibits the dynamic tricritical point and the reentrant behaviors.     

Some statistical properties for a spin-(1/2) particle coupled to two spirals

In this paper we consider the problem of the interaction between two SU(2) quantum systems namely: two-level atom and multi-level atoms. The evolution operator is obtained and used to calculate the time-dependent dynamical operators. It has shown that the atomic inversion is sensitive to the change in the detuning parameter ?, the quantum numbers j_k as well as the atomic angles. The atomic squeezing is also considered and the phenomenon of squeezing is observed in both quadrature variances, however, with a periodic exchange between the quadratures. The degree of entanglement is examined by employing von Neumann entropy. It has shown that an increase in the value of the detuning parameter leads to a decrease in the degree of entanglement. However, for a weak coupling parameter the system shows reduction in the entropy. In the meantime the maximum entanglement can be reached when we increase the value for the quantum numbers j_k. Also it has shown that the atomic angles play a role for controlling the degree of entanglement.     

The effect of anisotropies on the transition temperature in a spin-1/2 and spin-3/2 bilayer system with disordered interfaces

Transition temperatures of a bilayer system with A₂ (A_pB_1−p)₁ (B)₂ consisting periodically of two layers of spin-1/2 A atoms, two layers of spin-3/2 B atoms and an interface with alloying-type (A_pB_1−p) disorder are examined by the use of the effective-field theory superior to the standard mean-field theory. In particular, the effects of different single-ion anisotropies in the bulk B layers and disordered interfaces on the transition temperature are clarified. Some interesting behaviours are obtained, depending on the values of anisotropies and exchange interactions in the disordered interfaces and bulk layers.     

Dynamic compensation temperatures in a mixed spin-1 and spin-3/2 Ising system under a time-dependent oscillating magnetic field

We study the existence of dynamic compensation temperatures in the mixed spin-1 and spin-3/2 Ising ferrimagnetic system Hamiltonian with bilinear and crystal-field interactions in the presence of a time-dependent oscillating external magnetic field on a hexagonal lattice. We employ the Glauber transitions rates to construct the mean-field dynamic equations. We investigate the time dependence of an average sublattice magnetizations, the thermal behavior of the dynamic sublattice magnetizations and the total magnetization. From these studies, we find the phases in the system, and characterize the nature (continuous or discontinuous) of transitions as well as obtain the dynamic phase transition (DPT) points and the dynamic compensation temperatures. We also present dynamic phase diagrams, including the compensation temperatures, in the five different planes. A comparison is made with the results of the available mixed spin Ising systems.