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Honorary issue dedicated to the 70-th anniversary of Professor Ihor Stasyuk

On September 23, 2008 Professor Ihor Stasyuk, a prominent Ukrainian scientist, celebrates his 70th birthday. On this occasion, Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine and Editorial Board of "Condensed Matter Physics" decided to honour him with a collection of scientific papers. With great pleasure have numerous researchers, colleagues and coworkers of Prof. Stasyuk contributed their articles. The Editorial Board of "Condensed Matter Physics" expresses sincere gratitude to all of them. The highly skilled contributions deal with statistical theory of condensed matter, strongly correlated electron and spin systems, ferroelectrics and other areas which are close to the jubileer's interests during almost 50 years of his scientific activities.

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Title: Theory of radiation and absorption of deformed field quanta
Author(s):

I.O.Vakarchuk (Department for Theoretical Physics, Ivan Franko NationalUniversity of Lviv, Drahomanov Str. 12, Lviv 79005, Ukraine)

We calculate the intensity of spontaneous radiation of a system of non-linear quantum field, where the non-linearity is due to deformations of the Poison brackets of the generalized coordinates and momenta.

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Title: The second order phase transition in Sn₂P₂S₆ crystals: anharmonic oscillator model
Author(s):

	R.M.Yevych (Institute for Solid State Physics and Chemistry, Uzhgorod National University, Pidgirna Str., 46, Uzhgorod, 88000, Ukraine) ,
	Yu.M.Vysochanskii (Institute for Solid State Physics and Chemistry, Uzhgorod National University, Pidgirna Str., 46, Uzhgorod, 88000, Ukraine)

Statistical theory for ferroelectrics based on triple well anharmonic potential was used for the case of structural second order phase transition in Sn₂P₂S₆ crystals. Parameters of effective Hamiltonian of the model were estimated using available experimental data. These findings confirm the assumption that the phase transition in these crystals is located in crossover region between order-disorder and displacive type, and very closely to tricritical point.

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Title: F-electron spectral function of the Falicov-Kimball model and the Wiener-Hopf sum equation approach
Author(s):

	A.M.Shvaika (Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Str., 79011 Lviv, Ukraine) ,
	J.K.Freericks (Department of Physics, Georgetown University, 37th and O Sts. NW, Washington, DC 20057, USA)

We derive an alternative representation for the f-electron spectral function of the Falicov-Kimball model from the original one proposed by Brandt and Urbanek. In the new representation, all calculations are restricted to the real time axis, allowing us to go to arbitrarily low temperatures. The general formula for the retarded Green's function involves two determinants of continuous matrix operators that have the Toeplitz form. By employing the Wiener-Hopf sum equation approach and Szegö's theorem, we can derive exact analytic formulas for the large-time limits of the Green's function; we illustrate this for cases when the logarithm of characteristic function (which defines the continuous Toeplitz matrix) does and does not wind around the origin. We show how accurate these asymptotic formulas are to the exact solutions found from extrapolating matrix calculations to the zero discretization size limit.

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Title: Electron correlations in narrow energy bands: modified polar model approach
Author(s):

	L.Didukh (Ternopil State Technical University, Department of Physics, 56 Rus'ka Str., 46001 Ternopil, Ukraine) ,
	Yu.Skorenkyy (Ternopil State Technical University, Department of Physics, 56 Rus'ka Str., 46001 Ternopil, Ukraine) ,
	O.Kramar (Ternopil State Technical University, Department of Physics, 56 Rus'ka Str., 46001 Ternopil, Ukraine)

The electron correlations in narrow energy bands are examined within the framework of the modified form of polar model. This model permits to analyze the effect of strong Coulomb correlation, inter-atomic exchange and correlated hopping of electrons and explain some peculiarities of the properties of narrow-band materials, namely the metal-insulator transition with an increase of temperature, nonlinear concentration dependence of Curie temperature and peculiarities of transport properties of electronic subsystem. Using a variant of generalized Hartree-Fock approximation, the single-electron Green's function and quasi-particle energy spectrum of the model are calculated. Metal-insulator transition with the change of temperature is investigated in a system with correlated hopping. Processes of ferromagnetic ordering stabilization in the system with various forms of electronic DOS are studied. The static conductivity and effective spin-dependent masses of current carriers are calculated as a function of electron concentration at various DOS forms. The correlated hopping is shown to cause the electron-hole asymmetry of transport and ferromagnetic properties of narrow band materials.

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Title: Effective t-J model of pairing: singlet versus triplet
Author(s):

J.Spałek (Marian Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland)

The t-J model is regarded as a canonical model of spin-singlet pairing induced by the kinetic exchange interaction also responsible for an antiferromagnetic ordering in the strongly correlated narrow-band systems. In the orbitally degenerate systems both ferromagnetic and antiferromagnetic kinetic exchange interactions occur. I briefly review the analogy between the singlet and triplet types of pairing, as well as draw some general conclusions about the pairing induced by these exchange interactions. The general discussion is also illustrated with a concrete case of a two-dimensional lattice with the spin triplet pairing.

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Title: Evolution of quasistationary electron spectrum in open spherical quantum dot
Author(s):

	M.V.Tkach (Fedkovych Chernivtsi National University, 2, Kotsyubinskoho St., Chernivtsi, 58012, Ukraine) ,
	Ju.O.Seti (Fedkovych Chernivtsi National University, 2, Kotsyubinskoho St., Chernivtsi, 58012, Ukraine) ,
	O.M.Voitsekhivska (Fedkovych Chernivtsi National University, 2, Kotsyubinskoho St., Chernivtsi, 58012, Ukraine)

The evolution of electron quasistationary spectrum in open spherical quantum dot is under study within the effective mass and rectangular potential model. Within the framework of the S-matrix model the exact solution of Schrödinger equation is obtained in general analytical form. It is shown, for the first time, that the generalized resonance energies and widths introduced as the parameters defining the probability distribution function (over the energy or quasi momentum) of electron location in quantum dot, adequately characterize the evolution of its quasistationary states (contrary to the S-matrix poles) in the whole range of barrier thickness: from zero (free states) up to the infinity (stationary bound states are under the barrier and virtual and free states are above it).

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Title: X-ray photoelectron spectroscopy of Sn₂P₂S₆ crystals
Author(s):

	J.Grigas (Faculty of Physics, Vilnius University, Sauletekio 9/3, LT-10222 Vilnius, Lithuania) ,
	E.Talik (Institute of Physics, Silesian University, Universytetska 4, 40-007 Katowice, Poland) ,
	V.Lazauskas (Institute of Theoretical Physics and Astronomy, Vilnius University, Gostauto 12, LT-01108 Vilnius, Lithuania) ,
	Yu.M.Vysochanskii (Uzhgorod University, Pidhirna 46, 88000 Uzhgorod, Ukraine) ,
	R.Yevych (Uzhgorod University, Pidhirna 46, 88000 Uzhgorod, Ukraine) ,
	M.Adamiec (Institute of Physics, Silesian University, Universytetska 4, 40-007 Katowice, Poland) ,
	V.Nelkinas (Institute of Theoretical Physics and Astronomy, Vilnius University, Gostauto 12, LT-01108 Vilnius, Lithuania)

The paper presents the X-ray photoelectron spectra (XPS) of the valence band (VB) and of the core levels (CL) of uniaxial ferroelectric Sn₂P₂S₆ single crystals from different crystallographic planes in both paraelectric and ferroelectric phases. The XPS were measured with monochromatized Al K_α radiation in the energy range 0-1400 eV. The VB consists of five bands with the maxima between 3.3 eV and 14.5 eV below the Fermi level. Experimental energies of the VB and core levels are compared with the results of theoretical ab initio calculations of the molecular model of the Sn₂P₂S₆ crystal. The electronic structure of the VB is revealed. Ferroelectric phase transition changes the atom's charge and strength of the bonds, electronic structure of VB, width of CL lines and chemical shifts for the Sn, P and S states which are crystallographic plane-dependent.

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Title: Spin fluctuations and the "strange metal" behavior of a weakly doped antiferromagnet
Author(s):

	V.M.Loktev (Bogolyubov Institute for Theoretical Physics, Metrologichna Str. 14-b, Kyiv, 03680 Ukraine) ,
	V.Turkowski (Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211, USA)

We analyze the spectral properties of a phenomenological model for a weakly doped two-dimensional antiferromagnet, in which the carriers move within one of the two sublattices where they were introduced. Such a constraint results in the free carrier spectra with the maxima at k=(± π/2 , ± π/2) observed in some cuprates. We consider the spectral properties of the model by taking into account fluctuations of the spins in the antiferromagnetic background. We show that such fluctuations lead to a non-pole-like structure of the single-hole Green's function and these fluctuations can be responsible for some anomalous "strange metal" properties of underdoped cuprates in the nonsuperconducting regime.

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Title: Electronic spectrum and superconductivity in Hubbard model
Author(s):

	N.M.Plakida (Joint Institute for Nuclear Research, 141980 Dubna, Russia; Max-Planck-Institut für Physik Komplexer Systeme, D-01187 Dresden, Germany) ,
	V.S.Oudovenko (Joint Institute for Nuclear Research, 141980 Dubna, Russia; Rutgers University, Piscataway, New Jersey 08854, USA)

A microscopic theory of electronic spectrum and superconducting pairing within the Hubbard model is formulated. The Dyson equation for the normal and anomalous Green functions in terms of the Hubbard operators is derived by applying the Mori-type projection technique. The self-energy is evaluated in the noncrossing approximation for electron scattering on spin and charge fluctuations induced by kinematic interaction for Hubbard operators. Numerical results for electron dispersion in the strong correlation limit are presented. Superconducting pairing mediated by antiferromagnetic exchange and spin fluctuations is discussed.

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Title: Quantum phase transition: Van Vleck antiferromagnet in a magnetic field
Author(s):

	I.M.Ivanova (National National Technical University of Ukraine "KPI", Prosp. Pobedy 37, Kyiv 03056, Ukraine) ,
	V.M.Kalita (Institute of Physics of the National Academy of Science of Ukraine, Prosp. Nauki 46, Kyiv 03680, Ukraine) ,
	V.O.Pashkov (National Aviation University, Kosmonavta Komarova Ave. 1, Kyiv 03058, Ukraine) ,
	V.M.Loktev (Bogolyubov Institute for Theoretical Physics of the National Academy of Science of Ukraine, Metrolohichna Str. 14, Kyiv 03680, Ukraine)

Theoretical description of magnetic properties of antiferromagnetic state, induced by the longitudinal magnetic field, in the Van Vleck - singlet - magnet with single-ion anisotropy of "easy-plane" type and ion spin S=1 is proposed. It is shown that the quantum phase transition to the antiferromagnetic state is connected with the spontaneous appearance of spin polarization in the easy plane. Spin polarization of the ground non-degenerated state proves to be the order parameter of such a transition and the Landau thermodynamic approach can be employed for its (transition) description. The magnetic properties which include the field behavior of magnetization and magnetic susceptibility of the antiferromagnetic phase in the fields of different directions are studied. An attempt is made to qualitatively compare the obtained results with the available experimental data.

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Title: Thermodynamics and complex dielectric permittivity of mixed crystals of the Rb_1-x(NH₄)_xH₂PO₄ type
Author(s):

	R.R.Levitsky (Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Str, 79011 Lviv, Ukraine) ,
	S.I.Sorokov (Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Str, 79011 Lviv, Ukraine) ,
	J.Stankowski (Institute of Molecular Physics, Polish Academy of Sciences, Smoluchowskiego 17, 60-179 Poznan, Poland) ,
	Z.Trybula (Institute of Molecular Physics, Polish Academy of Sciences, Smoluchowskiego 17, 60-179 Poznan, Poland) ,
	A.S.Vdovych (Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Str, 79011 Lviv, Ukraine)

We propose a pseudospin model for proton glasses of the Rb_1-x(NH₄)_xH₂PO₄(Rb_1-x(ND₄)_xD₂PO₄) type, which takes into account the energy levels of hydrogens (deuterons) around the PO₄ group, long-range interactions between the hydrogen bonds, and an internal random deformational field. Within the framework of a cluster approximation and a mean field approximation over the long-range interactions, we derive a system of equations for the state parameters for the regions which are in the ferroelectric and antiferroelectric states, as well as in the proton glass state. Within the Glauber dynamics approach, we obtain a system of equations for the frequency-dependent linear responses of polarization and the proton glass order parameter. We obtain a qualitative description of the temperature behavior of dielectric permittivities of the K_1-x(ND₄)_xD₂PO₄ and
Rb_1-x(NH₄)_xH₂AsO₄ compounds at different frequencies. The origin of low-temperature peak in the imaginary part of dielectric permittivity in proton glasses is discussed.

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Title: Magnetic and thermal properties of a one-dimensional spin-1 model
Author(s):

	F.Mancini (Dipartimento di Fisica "E. R. Caianiello" - Unit\`a CNISM di Salerno, Universit\`a degli Studi di Salerno, Via S. Allende, I-84081 Baronissi (SA), Italy) ,
	F.P.Mancini (Dipartimento di Fisica and Sezione I.N.F.N., Universit\`a degli Studi di Perugia, Via A. Pascoli, I-06123 Perugia, Italy)

We study the one-dimensional S=1 Blume-Emery-Griffiths model. Upon transforming the spin model into an equivalent fermionic model, we provide the exact solution within the Green's function and equations of motion formalism. We show that the relevant response functions as well as thermodynamic quantities can be determined, in the whole parameters space, in terms of a finite set of local correlators. Furthermore, considering the case of an antiferromagnetic chain with single-ion anisotropy in the presence of an external magnetic field, we find three plateaus in the magnetization curve. In the neighborhood of the endpoints of the intermediate plateau, the specific heat shows a double peak structure.

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Title: Longitudinal relaxation of mechanically free KH₂PO₄ type crystals. Piezoelectric resonance and sound attenuation
Author(s):

	R.R.Levitskii (Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Str., 79011 Lviv, Ukraine) ,
	I.R.Zachek (Lviv Polytechnic National University, 12 Bandera Str., 79013 Lviv, Ukraine) ,
	A.P.Moina (Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Str., 79011 Lviv, Ukraine) ,
	A.S.Vdovych (Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Str., 79011 Lviv, Ukraine)

Within the framework of proton model with taking into account the piezoelectric interaction with the shear strain ε₆, a dynamic dielectric response of KD₂PO₄ type ferroelectrics is considered. Experimentally observed phenomena of crystal clamping by high frequency electric field, piezoelectric resonance and microwave dispersion are described. Ultrasound velocity and attenuation are calculated, peculiarities of their temperature dependence at the Curie points are described. Existence of a cut-off frequency in the frequency dependence of attenuation is predicted.

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Title: External field effect on the anisotropy of dielectric permeability of KH₂PO₄ and NaKC₄H₄O₆· 4H₂O crystals under high pressure
Author(s):

	A.G.Slivka (Uzhhorod National University, Department of Optics, 54 Voloshyn Str., 88000, Uzhhorod, Ukraine) ,
	V.M.Kedyulich (Uzhhorod National University, Department of Optics, 54 Voloshyn Str., 88000, Uzhhorod, Ukraine) ,
	H.M.Guyvan (Uzhhorod National University, Department of Optics, 54 Voloshyn Str., 88000, Uzhhorod, Ukraine)

Experimental studies of the effect of temperature, external pressure and electric field on the anisotropy of dielectric permeability of KH₂PO₄ and NaKC₄H₄O₆· 4H₂O crystals are performed. The experimental data on the effect of electric field and pressure on the dielectric permeability of Rochelle salt are analyzed in the framework of phenomenological theory with the account of the vicinity of the phase transitions to the double critical point. Coefficients of thermodynamic potential expansion over the order parameter are determined as well as its pressure behaviour is described. The hydrostatic pressure increase is shown to shift the phase transitions in Rochelle salt away from the double critical point.