T. Balcerzak

Phase diagram of a spin-1 magnetic bilayer by cluster variational theory: Exact results for a BEG model on a Bethe lattice with five-fold coordination

Abstract The complete global phase diagram for a magnetic spin-1 bilayer, whose interactions are described by the Blume Emery Griffiths model (BEG), is studied by cluster variational theory within the pair approximation. The results obtained, are also the exact results pertaining to the BEG model on a Bethe lattice having coordination number, z =5. Useful analytic expressions are derived for trajectories in phase space containing the second-order (continuous) phase boundaries. The physical existence of these second-order boundaries, together with the location of the first-order phase boundaries, are determined from a Gibbs free energy analysis. Detailed comparison of the results with those of other workers on this, and closely related systems, is made.

The ising-heisenberg two-atom cluster approximation of a ferromagnet (S = 12)

Abstract In the paper the two-atom cluster model with two Heisenberg spins in the Ising surrounding has been proposed for the description of the Heisenberg ferromagnet. In the frame of this model the general set of two equations has been derived, hence the J/kT c value, the magnetization curve, the correlation function between n.n. spins, the magnetic contribution to specific heat and magnetic susceptibility have been calculated for the particular case of a ferromagnet with sc symmetry.

The magnetization of thin ferromagnetic film in Ising approximation (S = 12)☆

Abstract In the paper thin ferromagnetic films with perfect crystal structure and with structure of diluted alloy have been considered. For both cases the magnetization profiles across the film for various temperatures and various film thicknesses, together with the corresponding critical temperatures have been calculated. For the case of film with diluted alloy structure the relation of critical concentration of magnetic atoms on film thickness has been also found.

CLUSTER IDENTITIES IN LOCALIZED SPIN SYSTEMS

Abstract A general method of derivation of various statistical identities for localized spin systems is presented. It is shown how a number of effective field approximations can be obtained from these identities. The operator transformation techniques are also presented, which markedly improve the accuracy of the calculations and widen the possibilities of various applications of those identities.

Phase transitions of a spin-one magnetic film

Abstract A cluster variational method is developed and applied in a study of a spin 1 BEG model of a magnetic film. The phase diagrams for films of different thickness are determined and essential differences between them and those predicted by mean field theory are highlighted.

A simple method of basic properties description of diluted ferromagnetic alloys (Ising model, S = 12

Abstract A simple method of basic magnetic properties description of diluted ferromagnetic alloys with S = 1 2 is discussed for the case of Ising approximation. As a result the relations for magnetization curve, internal energy, magnetic contribution to specific heat and magnetic susceptibility have been obtained for arbitrary concentration c of magnetic atoms. As an illustration the corresponding curves, calculated for several values of c , have been also presented.

On the exact identities for Ising model with arbitrary spin

Abstract The exact Callen–Suzuki statistical identities for the Ising model with arbitrary spin S are discussed. In particular, the recursion method for obtaining the arbitrary-order moments is shown. The concept of projection operator is employed for studies of the reduction of the high-order moments, as well as for the van der Waerden identities. Also, the integral operator method is extended for the model in question. The obtained exact formulas are discussed from the point of view of their practical applicability.

Antiferromagnetic interlayer coupling in diluted magnetic thin films with RKKY interaction

We study a model thin film containing diluted bilayer structure with the Ruderman-Kittel-Kasuya-Yosida long-range interaction. The magnetic subsystem is composed of two magnetically doped layers, separated by an undoped nonmagnetic spacer, and placed inside a wider film modeled by a quantum well of infinite depth. We focus our study on the range of parameters for which the antiferromagnetic coupling between the magnetic layers can be expected. The critical temperatures for such system are found and their dependence on magnetic layer thickness and charge-carrier concentration is discussed. The magnetization distribution within each magnetic layer is calculated as a function of layer thickness. The external field required to switch the mutual orientation of layer magnetizations from antiferromagnetic to ferromagnetic state is also discussed.

The magnetisation and the correlation functions in thin diluted films (ising model, S=1/2)

The thin diluted ferromagnetic film with SC symmetry is considered in the third-order Matsudaira approximation. The equations for the description of magnetisation and various correlation functions have been derived and the results of the numerical calculations have been presented. In particular the critical temperature, the critical concentration, the magnetisation and various correlation functions are discussed in detail for various film thicknesses and for several magnetic atom concentrations.

Thermodynamics of the Ising model in pair approximation

A complete thermodynamic description for the Ising model in the pair approximation is given. The minimisation of the Gibbs energy is performed with respect to the magnetisation and nearest-neighbour correlation function, treated as the variational parameters. The results are discussed and illustrated in the figures.