Tadeusz Balcerzak - Academia.edu (original) (raw)

Papers by Tadeusz Balcerzak

Research paper thumbnail of Ising Model with Random Local Fields in a Two-Dimensional Ferromagnet

physica status solidi (b), 1989

ABSTRACT A spin 1/2 Ising model with random fields is studied using a 3-rd order Matsudaira appro... more ABSTRACT A spin 1/2 Ising model with random fields is studied using a 3-rd order Matsudaira approximation. The two-dimensional ferromagnet with square lattice is considered only. The system is found to show a tricritical behaviour and the existence of two phase transitions, one of second order and another of first order, for certain values of the field strength. The behaviour of magnetization and spin-correlation function between n.n. spins is discussed in detail.Mit der Matsudaira-Näherung dritter Ordnung wird das Ising-Modell für Spin 1/2 bei statistischen Feldern untersucht. Nur der zweidimensionale Ferromagnet mit quadratischem Gitter wird betrachtet. Es wird gefunden, daß das System trikritisches Verhalten und die Existenz von zwei Phasenübergängen, einer von zweiter Ordnung und ein anderer von erster Ordnung, für bestimmte Werte der Feldstärke zeigt. Das Verhalten der Magnetisierung und der Spin-Korrelationsfunktion zwischen n.n.-Spins wird ausführlich diskutiert.

Research paper thumbnail of Exact studies of the ground-state properties of the anisotropic Heisenberg dimer with spin S=1

Journal of Magnetism and Magnetic Materials

Research paper thumbnail of Magnetization curves of spin- Ising thin films with spin- overlayers

Physica A: Statistical Mechanics and its Applications, 1994

ABSTRACT

Research paper thumbnail of The Curie temperature of thin films; the role of anisotropy at the surfaces

Physica A: Statistical Mechanics and its Applications, 1993

The ferromagnetic phase transition in thin films consisting of spin-f-Ising layers with spin-$ ov... more The ferromagnetic phase transition in thin films consisting of spin-f-Ising layers with spin-$ overlayers is studied by the use of the effective-held theory superior to the standard mean-field theory. The model calculation shows that the Curie temperature severely depends on the value of the single-ion anisotropy D at the surfaces, namely inplane (D < 0) or perpendicular (D >O), as well as the thickness and the interactions at and with the surfaces.

Research paper thumbnail of The influence of anharmonic interactions and external force on the surface roughness

Surface Science, 1994

Abstract The influence of anharmonic interactions and external force on the surface roughness is ... more Abstract The influence of anharmonic interactions and external force on the surface roughness is studied in the frame of the extended discrete Gaussian model. The method is based on the local statistical identities with correlations. The roughness parameter and the contribution to the specific heat have been calculated for the regular lattice over a wide range of temperatures. For the negative anharmonic interactions a new roughening phase transition has been found.

Research paper thumbnail of Discretization of the Fermi surface in thin films

Thin Solid Films, 2006

The thin film model in free-electron approximation is considered. A discrete Fermi surface is con... more The thin film model in free-electron approximation is considered. A discrete Fermi surface is constructed depending on the film thickness and electron density. The Fermi wavevector, the mean energy per one electron and the density of states at the Fermi surface are calculated for the films with various thicknesses and different crystallographic orientation.

Research paper thumbnail of Paramagnetic electronic susceptibility of the thin films

Thin Solid Films, 2006

The thin film model, based on a concept of 1D quantum well, in the free-electron approximation is... more The thin film model, based on a concept of 1D quantum well, in the free-electron approximation is considered. The analytical expression for the paramagnetic electronic susceptibility is derived in the first order of perturbation calculus. The numerical calculations of paramagnetic susceptibility for various transversal modes of molecular field are presented in figures and discussed.

Research paper thumbnail of The Magnetic Phase Diagram of EuTe for High External Pressure

physica status solidi (b), 2001

Research paper thumbnail of Ground-state phase diagrams of the mixed ferro-ferrimagnetic ternary alloy with a single-ion anisotropy

Physica A: Statistical Mechanics and its Applications, 2003

... interest in the synthesis and study of the magnetic properties of molecular-based magnetic ma... more ... interest in the synthesis and study of the magnetic properties of molecular-based magnetic materials [1], [2], [3], [4], [5] and [6]. Among these compounds, a particular interest has been paid to multi-metal Prussian blue analogs such as (A p II Mn 1−p II ) 1.5 [Cr III (CN) 6 ]·zH 2 O ...

Research paper thumbnail of Thermodynamics of the Ising model in pair approximation

Physica A: Statistical Mechanics and its Applications, 2003

A complete thermodynamic description for the Ising model in the pair approximation is given. The ... more 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.

Research paper thumbnail of The magnetization and the spin-correlation functions in a thin ferromagnetic film (Ising model, )

Journal of Magnetism and Magnetic Materials, 1988

In the paper the method of calculation of thin-film magnetization and two-spin correlation functi... more In the paper the method of calculation of thin-film magnetization and two-spin correlation functions is developed. The numerical results for film with SC symmetry and composed to two atomic layers are presented. As it has been shown the correlation functions depend not only on the distance between the spin-pair but also on the position of the pair in the sample.

Research paper thumbnail of Phase transitions of a spin-one magnetic film

Journal of Magnetism and Magnetic Materials, 1995

Abstract A cluster variational method is developed and applied in a study of a spin 1 BEG model o... more 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.

Research paper thumbnail of Phase diagrams of the Blume–Emery–Griffiths model with site dilution

Journal of Magnetism and Magnetic Materials, 2001

Cluster variational method in pair approximation has been extended for the description of the sit... more Cluster variational method in pair approximation has been extended for the description of the site-diluted Blume}Emery}Gri!ths model with spin 1. The phase diagrams for the case of dilution are discussed in the presence of biquadratic interactions and single-ion anisotropy. In particular, the critical concentrations for the ferromagnetic and staggered quadrupolar phases, as well as the shift of tricritical point as a result of dilution have been studied. The numerical calculations are presented for a bilayer system with the coordination number z"5.

Research paper thumbnail of Some magnetic properties of the diluted square ising lattice with fluctuating exchange integrals

Journal of Magnetism and Magnetic Materials, 1990

The site-and bond-disordered ferromagnet is examined with the use of the 1st and 3rd Matsudaira a... more The site-and bond-disordered ferromagnet is examined with the use of the 1st and 3rd Matsudaira approxivaations. As a result, the phase diagrams, the magnetization curves and the correlation functions between nearest neighbour spins for various c and A parameters, characterizing the dilution and the fluctuations of the exchange integral, are discussed in detail.

Research paper thumbnail of Thermodynamics of the small clusters: The Gibbs free-energy derivation for the Honmura–Kaneyoshi method

Journal of Magnetism and Magnetic Materials, 2008

A cluster density matrix is proposed for calculation of the thermodynamic averages in the effecti... more A cluster density matrix is proposed for calculation of the thermodynamic averages in the effective field theory with correlations. On this basis, derivation of the Gibbs free-energy for the Honmura–Kaneyoshi method is made.

Research paper thumbnail of Application of the pair approximation method for the RKKY interaction

Journal of Magnetism and Magnetic Materials, 2004

The pair approximation method for spin S ¼ 1 2 has been applied for the case of the long-range RK... more The pair approximation method for spin S ¼ 1 2 has been applied for the case of the long-range RKKY interaction on FCC lattice. The magnetization, Curie temperature and correlation function have been calculated for the range of interaction up to 185 coordination zones (10 lattice constants).

Research paper thumbnail of Random-field Ising model with second-neighbour interaction

Journal of Magnetism and Magnetic Materials, 1993

Abstract A random-field Ising model with second-neighbour interaction has been investigated using... more Abstract A random-field Ising model with second-neighbour interaction has been investigated using the new effective-field theory. The phase diagrams are examined in detail for the square lattice in a random field obeying the bimodal symmetric distribution. A tricritical point is found in the system, in contrast to the corresponding nearest-neighbour interaction Ising model. In particular, the tricritical phase diagram for a body-centered cubic lattice in nearest-neighbour approximation is also determined.

Research paper thumbnail of Cluster identities in localized spin systems

Journal of Magnetism and Magnetic Materials, 1991

Abstract A general method of derivation of various statistical identities for localized spin syst... more 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.

Research paper thumbnail of On the exact identities for Ising model with arbitrary spin

Journal of Magnetism and Magnetic Materials, 2002

The exact Callen-Suzuki statistical identities for the Ising model with arbitrary spin S are disc... more 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.

Research paper thumbnail of A comparison of the RKKY interaction for the 2D and 3D systems and thin films

Journal of Magnetism and Magnetic Materials, 2007

The formula for the RKKY exchange interaction in thin films is obtained in the frame of the free-... more The formula for the RKKY exchange interaction in thin films is obtained in the frame of the free-electron model. The numerical calculations based on this formula are presented for some exemplary thin films and compared with those for 2D and 3D systems.

Research paper thumbnail of Ising Model with Random Local Fields in a Two-Dimensional Ferromagnet

physica status solidi (b), 1989

ABSTRACT A spin 1/2 Ising model with random fields is studied using a 3-rd order Matsudaira appro... more ABSTRACT A spin 1/2 Ising model with random fields is studied using a 3-rd order Matsudaira approximation. The two-dimensional ferromagnet with square lattice is considered only. The system is found to show a tricritical behaviour and the existence of two phase transitions, one of second order and another of first order, for certain values of the field strength. The behaviour of magnetization and spin-correlation function between n.n. spins is discussed in detail.Mit der Matsudaira-Näherung dritter Ordnung wird das Ising-Modell für Spin 1/2 bei statistischen Feldern untersucht. Nur der zweidimensionale Ferromagnet mit quadratischem Gitter wird betrachtet. Es wird gefunden, daß das System trikritisches Verhalten und die Existenz von zwei Phasenübergängen, einer von zweiter Ordnung und ein anderer von erster Ordnung, für bestimmte Werte der Feldstärke zeigt. Das Verhalten der Magnetisierung und der Spin-Korrelationsfunktion zwischen n.n.-Spins wird ausführlich diskutiert.

Research paper thumbnail of Exact studies of the ground-state properties of the anisotropic Heisenberg dimer with spin S=1

Journal of Magnetism and Magnetic Materials

Research paper thumbnail of Magnetization curves of spin- Ising thin films with spin- overlayers

Physica A: Statistical Mechanics and its Applications, 1994

ABSTRACT

Research paper thumbnail of The Curie temperature of thin films; the role of anisotropy at the surfaces

Physica A: Statistical Mechanics and its Applications, 1993

The ferromagnetic phase transition in thin films consisting of spin-f-Ising layers with spin-$ ov... more The ferromagnetic phase transition in thin films consisting of spin-f-Ising layers with spin-$ overlayers is studied by the use of the effective-held theory superior to the standard mean-field theory. The model calculation shows that the Curie temperature severely depends on the value of the single-ion anisotropy D at the surfaces, namely inplane (D < 0) or perpendicular (D >O), as well as the thickness and the interactions at and with the surfaces.

Research paper thumbnail of The influence of anharmonic interactions and external force on the surface roughness

Surface Science, 1994

Abstract The influence of anharmonic interactions and external force on the surface roughness is ... more Abstract The influence of anharmonic interactions and external force on the surface roughness is studied in the frame of the extended discrete Gaussian model. The method is based on the local statistical identities with correlations. The roughness parameter and the contribution to the specific heat have been calculated for the regular lattice over a wide range of temperatures. For the negative anharmonic interactions a new roughening phase transition has been found.

Research paper thumbnail of Discretization of the Fermi surface in thin films

Thin Solid Films, 2006

The thin film model in free-electron approximation is considered. A discrete Fermi surface is con... more The thin film model in free-electron approximation is considered. A discrete Fermi surface is constructed depending on the film thickness and electron density. The Fermi wavevector, the mean energy per one electron and the density of states at the Fermi surface are calculated for the films with various thicknesses and different crystallographic orientation.

Research paper thumbnail of Paramagnetic electronic susceptibility of the thin films

Thin Solid Films, 2006

The thin film model, based on a concept of 1D quantum well, in the free-electron approximation is... more The thin film model, based on a concept of 1D quantum well, in the free-electron approximation is considered. The analytical expression for the paramagnetic electronic susceptibility is derived in the first order of perturbation calculus. The numerical calculations of paramagnetic susceptibility for various transversal modes of molecular field are presented in figures and discussed.

Research paper thumbnail of The Magnetic Phase Diagram of EuTe for High External Pressure

physica status solidi (b), 2001

Research paper thumbnail of Ground-state phase diagrams of the mixed ferro-ferrimagnetic ternary alloy with a single-ion anisotropy

Physica A: Statistical Mechanics and its Applications, 2003

... interest in the synthesis and study of the magnetic properties of molecular-based magnetic ma... more ... interest in the synthesis and study of the magnetic properties of molecular-based magnetic materials [1], [2], [3], [4], [5] and [6]. Among these compounds, a particular interest has been paid to multi-metal Prussian blue analogs such as (A p II Mn 1−p II ) 1.5 [Cr III (CN) 6 ]·zH 2 O ...

Research paper thumbnail of Thermodynamics of the Ising model in pair approximation

Physica A: Statistical Mechanics and its Applications, 2003

A complete thermodynamic description for the Ising model in the pair approximation is given. The ... more 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.

Research paper thumbnail of The magnetization and the spin-correlation functions in a thin ferromagnetic film (Ising model, )

Journal of Magnetism and Magnetic Materials, 1988

In the paper the method of calculation of thin-film magnetization and two-spin correlation functi... more In the paper the method of calculation of thin-film magnetization and two-spin correlation functions is developed. The numerical results for film with SC symmetry and composed to two atomic layers are presented. As it has been shown the correlation functions depend not only on the distance between the spin-pair but also on the position of the pair in the sample.

Research paper thumbnail of Phase transitions of a spin-one magnetic film

Journal of Magnetism and Magnetic Materials, 1995

Abstract A cluster variational method is developed and applied in a study of a spin 1 BEG model o... more 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.

Research paper thumbnail of Phase diagrams of the Blume–Emery–Griffiths model with site dilution

Journal of Magnetism and Magnetic Materials, 2001

Cluster variational method in pair approximation has been extended for the description of the sit... more Cluster variational method in pair approximation has been extended for the description of the site-diluted Blume}Emery}Gri!ths model with spin 1. The phase diagrams for the case of dilution are discussed in the presence of biquadratic interactions and single-ion anisotropy. In particular, the critical concentrations for the ferromagnetic and staggered quadrupolar phases, as well as the shift of tricritical point as a result of dilution have been studied. The numerical calculations are presented for a bilayer system with the coordination number z"5.

Research paper thumbnail of Some magnetic properties of the diluted square ising lattice with fluctuating exchange integrals

Journal of Magnetism and Magnetic Materials, 1990

The site-and bond-disordered ferromagnet is examined with the use of the 1st and 3rd Matsudaira a... more The site-and bond-disordered ferromagnet is examined with the use of the 1st and 3rd Matsudaira approxivaations. As a result, the phase diagrams, the magnetization curves and the correlation functions between nearest neighbour spins for various c and A parameters, characterizing the dilution and the fluctuations of the exchange integral, are discussed in detail.

Research paper thumbnail of Thermodynamics of the small clusters: The Gibbs free-energy derivation for the Honmura–Kaneyoshi method

Journal of Magnetism and Magnetic Materials, 2008

A cluster density matrix is proposed for calculation of the thermodynamic averages in the effecti... more A cluster density matrix is proposed for calculation of the thermodynamic averages in the effective field theory with correlations. On this basis, derivation of the Gibbs free-energy for the Honmura–Kaneyoshi method is made.

Research paper thumbnail of Application of the pair approximation method for the RKKY interaction

Journal of Magnetism and Magnetic Materials, 2004

The pair approximation method for spin S ¼ 1 2 has been applied for the case of the long-range RK... more The pair approximation method for spin S ¼ 1 2 has been applied for the case of the long-range RKKY interaction on FCC lattice. The magnetization, Curie temperature and correlation function have been calculated for the range of interaction up to 185 coordination zones (10 lattice constants).

Research paper thumbnail of Random-field Ising model with second-neighbour interaction

Journal of Magnetism and Magnetic Materials, 1993

Abstract A random-field Ising model with second-neighbour interaction has been investigated using... more Abstract A random-field Ising model with second-neighbour interaction has been investigated using the new effective-field theory. The phase diagrams are examined in detail for the square lattice in a random field obeying the bimodal symmetric distribution. A tricritical point is found in the system, in contrast to the corresponding nearest-neighbour interaction Ising model. In particular, the tricritical phase diagram for a body-centered cubic lattice in nearest-neighbour approximation is also determined.

Research paper thumbnail of Cluster identities in localized spin systems

Journal of Magnetism and Magnetic Materials, 1991

Abstract A general method of derivation of various statistical identities for localized spin syst... more 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.

Research paper thumbnail of On the exact identities for Ising model with arbitrary spin

Journal of Magnetism and Magnetic Materials, 2002

The exact Callen-Suzuki statistical identities for the Ising model with arbitrary spin S are disc... more 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.

Research paper thumbnail of A comparison of the RKKY interaction for the 2D and 3D systems and thin films

Journal of Magnetism and Magnetic Materials, 2007

The formula for the RKKY exchange interaction in thin films is obtained in the frame of the free-... more The formula for the RKKY exchange interaction in thin films is obtained in the frame of the free-electron model. The numerical calculations based on this formula are presented for some exemplary thin films and compared with those for 2D and 3D systems.