In honour of Professor Ihor Yukhnovskii on the occasion of his 75th birthday
The present and the preceding issues of “Condensed Matter Physics” contain papers written in honour of Professor Ihor Yukhnovskii on the occasion of his 75th birthday. Professor Ihor Yukhnovskii is a well-known Ukrainian physicist, statesman and public figure. He is a founder of the Lviv school o...
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Інститут фізики конденсованих систем НАН України
2000
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irk-123456789-1212662017-06-14T03:07:02Z In honour of Professor Ihor Yukhnovskii on the occasion of his 75th birthday The present and the preceding issues of “Condensed Matter Physics” contain papers written in honour of Professor Ihor Yukhnovskii on the occasion of his 75th birthday. Professor Ihor Yukhnovskii is a well-known Ukrainian physicist, statesman and public figure. He is a founder of the Lviv school of statistical physics. Its main directions are the theory of liquids and electrolyte solutions, the theory of quantum systems of interacting particles, the theory of phase transitions and critical phenomena, theory of disordered systems and the theory of nonequilibrium processes. 2000 Article In honour of Professor Ihor Yukhnovskii on the occasion of his 75th birthday // Condensed Matter Physics. — 2000. — Т. 3, № 3(23). — С. 697-708. — англ. 1607-324X http://dspace.nbuv.gov.ua/handle/123456789/121266 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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The present and the preceding issues of “Condensed Matter Physics” contain
papers written in honour of Professor Ihor Yukhnovskii on the occasion of his 75th
birthday. Professor Ihor Yukhnovskii is a well-known Ukrainian physicist, statesman
and public figure. He is a founder of the Lviv school of statistical physics. Its main
directions are the theory of liquids and electrolyte solutions, the theory of quantum
systems of interacting particles, the theory of phase transitions and critical phenomena,
theory of disordered systems and the theory of nonequilibrium processes. |
| format |
Article |
| title |
In honour of Professor Ihor Yukhnovskii on the occasion of his 75th birthday |
| spellingShingle |
In honour of Professor Ihor Yukhnovskii on the occasion of his 75th birthday Condensed Matter Physics |
| title_short |
In honour of Professor Ihor Yukhnovskii on the occasion of his 75th birthday |
| title_full |
In honour of Professor Ihor Yukhnovskii on the occasion of his 75th birthday |
| title_fullStr |
In honour of Professor Ihor Yukhnovskii on the occasion of his 75th birthday |
| title_full_unstemmed |
In honour of Professor Ihor Yukhnovskii on the occasion of his 75th birthday |
| title_sort |
in honour of professor ihor yukhnovskii on the occasion of his 75th birthday |
| publisher |
Інститут фізики конденсованих систем НАН України |
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2000 |
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http://dspace.nbuv.gov.ua/handle/123456789/121266 |
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In honour of Professor Ihor Yukhnovskii on the occasion of his 75th birthday // Condensed Matter Physics. — 2000. — Т. 3, № 3(23). — С. 697-708. — англ. |
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Condensed Matter Physics |
| first_indexed |
2025-07-08T19:30:07Z |
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1837108308858634240 |
| fulltext |
Condensed Matter Physics, 2000, Vol. 3, No. 3(23), pp. 697–708
In honour of Professor Ihor Yukhnovskii
on the occasion of his 75th birthday
The present and the preceding issues of “Condensed Matter Physics” contain
papers written in honour of Professor Ihor Yukhnovskii on the occasion of his 75th
birthday. Professor Ihor Yukhnovskii is a well-known Ukrainian physicist, statesman
and public figure. He is a founder of the Lviv school of statistical physics. Its main
directions are the theory of liquids and electrolyte solutions, the theory of quantum
systems of interacting particles, the theory of phase transitions and critical phenom-
ena, theory of disordered systems and the theory of nonequilibrium processes.
The research activity of Ihor Yukhnovskii is closely connected with the name
of prominent scientist – Professor N.N.Bogoliubov. Permanent scientific contacts
between I.R.Yukhnovskii and N.N.Bogoliubov generated new ideas and solutions of
specific physical problems and promoted forming the main scientific directions of
Lviv school of statistical physics.
The first papers of Ihor Yukhnovskii were published in collaboration with Profes-
sor A.E.Glauberman, who was a supervisor of his Ph.D. work. The main subject of
this study was related to applications of Bogoliubov’s method of plasma parameter
expansion for the study of binary distribution functions in charged particle systems.
The results obtained were used in the theory of electrolyte solutions as well as in
the theory of the high-temperature plasma.
The method of collective variables developed by I.R.Yukhnovskii permitted to
consider one of the central problems in statistical physics: the problem of a correct
and simultaneous treatment of the short- and long-range interactions in classical
systems of interacting particles. Description of statistical systems in an extended
phase space containing coordinates of particles and modes of density fluctuations
(collective variables) is the main idea of this approach. Transition to the extended
phase space is performed by means of the transition function, its explicit form was
found. Two approaches were proposed by I.R.Yukhnovskii to take into consideration
the short-range interaction. The first one based on the functional differentiation is
reduced to the generalized Mayer group expansions for charged particle systems.
The second approach consists in the separation of the short-range interaction con-
tribution and in consideration of the screened long-range interactions. The latter
approach appeared to be the particular useful in constructing the theory of con-
densed matter, namely, the theory of liquids and electrolyte solutions.
In the 60th the method of collective variables first was extended to the ion-dipole
systems and then was generalized to the systems with arbitrary electrostatic interac-
697
In honour of Professor Ihor Yukhnovskii. . .
tions. The microscopic theory of electrolyte solutions elaborated by I.R.Yukhnovskii
and M.F.Holovko was the most important achievement in this field. The use of
the high-order group expansions enabled one to study the fundamental role of the
molecular subsystem in revealing (on the microscopic level) both the nature of
the ion solvation and a peculiarity of the short-range order in electrolyte solutions
(I.R.Yukhnovskii, M.F.Holovko, A.O.Nekrot, V.S.Vysochanskii).
In the works of I.R.Yukhnovskii, M.F.Holovko, I.Y.Kuryliak, and Ye.M.Soviak,
the theory of electrolyte solutions was extended to the case of spatially bounded
systems. Analytical theories for electrolyte mixtures and membranes were suggested.
It was found that screening effects for spatially nonuniform systems are qualitatively
different from those of bulk systems. The difference is caused by the presence of
electrostatic reflection forces in the electrolyte near the interface with the other
medium, which rouses adsorption effects. The phenomena of electrolyte ion repulsion
from (or attraction to) the surface were proven to depend on dielectric properties
of solvents and of the external medium. On the basis of the results obtained a new
mechanism of the desalination of water was proposed.
In 1964 I.R.Yukhnovskii initiated studies in the theory of interacting quantum
particles. He suggested and developed a new original approach: the method of dis-
placements and collective variables. This method is free of some intrinsic drawbacks
of other methods of many-body theory. The essence of the method is extraction
from the evolution operator, which is defined on the set of Cartesian particle co-
ordinates, a full multiplication operator that describes the interaction of quantum
particle wave packets and is expressed in terms of collective variables. From the
mathematical point of view this method maps the partition function of quantum
system on the partition function of classical system with many-particle interactions.
The method was applied to one of the most important models in the solid state the-
ory – an electron gas in a uniform compensating field (L.F.Blazhyjevskii, G.I.Bigun,
M.V.Vavrukh, R.M.Petrashko, P.P.Kostrobij).
Important results in the theory of strongly correlated electronic systems were
obtained by a follower of I.R.Yukhnovskii – Professor I.V.Stasyuk. In the mid-60ties
the original approach to the consideration of the short-range correlations based on
the formalism of site operators (Hubbard operators) was developed in his works.
On this basis numerous physical effects in crystals with ferroelectric and structural
phase transitions as well as in the systems with high-temperature superconductivity
were studied by Prof. I.V. Stasyuk and his collaborators.
The method of a reference system, proposed by Ihor Yukhnovskii, was employed
in the studies of various physical systems. For the reference system an accurate
solution can be found. This allows one to consider a whole system on the back-
ground of a reference one and to reformulate a perturbation theory on this basis. The
method of a reference system was successfully applied for the studies of hydrogen-
bonded ferroelectrics of the KDP type with taking into account the tunnelling effects
(I.R.Yukhnovskii and R.R.Levitskii). For the first time it was shown, that in the ref-
erence approach, with the short-range interactions and tunnelling taken into account
in cluster approximation, the dynamic properties of the studied systems were to a
698
In honour of Professor Ihor Yukhnovskii. . .
great extent determined by an effective tunnelling parameter, renormalized by the
short-range interactions.
A separate branch in the development of the displacements and collective vari-
ables method is connected with the studies of interacting systems of Bose-particles
(I.R.Yukhnovskii, I.O.Vakarchuk). These studies resulted in the construction of a
quantitative microscopic theory of 4He. An accurate expression for statistical op-
erator of the many-boson system in coherent states representation was found in
subsequent works by Professor I.O.Vakarchuk. There, an effective functional of the
grand canonical potential was found rigorously. This permitted to define a set of
λ-transition characteristics in liquid 4He.
Fundamental results were obtained by Ihor Yukhnovskii in the theory of phase
transitions and critical phenomena. His first papers in that direction were published
in the mid-70th and contained already the basic ideas of an original method for cal-
culating a partition function of a three dimensional Ising model within the collective
variables approach. It was shown (I.R.Yukhnovskii and Yu.K.Rudavskii) that the
consistent theory of phase transitions should be based on non-Gaussian measures of
critical fluctuations. Two main fluctuational processes with different space-scale were
discovered. The first one, called critical regime, has intrinsic renormalization group
symmetry and forms universal quantities such as critical exponents and ratios of crit-
ical amplitudes. And the second one, which was called the limiting Gaussian regime,
provides the thermodynamic stability of a system and is described by the renormal-
ized Gaussian distribution of fluctuations. On this basis explicit expressions for the
free energy, the specific heat and other thermodynamic quantities of the Ising model
in the vicinity of phase transition were obtained (I.R.Yukhnovskii, M.P.Kozlovskii,
V.O.Kolomiets, and I.V.Pylyuk) and the dependence of non-universal characteristics
on microscopic parameters was studied.
Taking into account the novelty of the Yukhnovskii’s approach, comparison of it
with other methods was made. In particular, I.R.Yukhnovskii, M.P.Kozlovskii and
Ya.M.Ilnitskii performed a comparative analysis of the collective variables method
and the ǫ-expansion approach. They found a series of essential advantages of the
collective variables method and the specific conditions at which the recursion re-
lations between the coefficients of effective block structures can be reduced to the
well-known K.Wilson’s recursion relations.
The detailed study of the Ising model critical behaviour enabled one to general-
ize I.R.Yukhnovskii’s approach to many other condensed systems, in particular, to
the study of the phase transition in the n-component model of a ferromagnet. The
first papers in that direction were published by I.O.Vakarchuk, Yu.K.Rudavskii and
I.R.Yukhnovskii in 1979. They suggested a functional representation of the partition
function of the n-component model and wrote down a differential form of the recur-
rent relations for this model. This became a basis for a further development of this
theoretical approach in the papers by Yu.V.Holovatch and I.M.Mryglod. Numerical
calculations for both the Ising model and the n-component model were made by
V.O.Kolomiets. Critical behaviour of disordered systems was studied in collabora-
tion with Yu.V.Holovatch and M.A.Shpot.
699
In honour of Professor Ihor Yukhnovskii. . .
A broad spectrum of studies was performed by Yukhnovskii’s disciples,
I.O.Vakarchuk and Yu.K.Rudavskii for topologically disordered magnetic systems.
The functional approach developed in their papers was applied to the study of
amorphous Heisenberg ferromagnets with liquid-like structure, including a vicinity
of the phase transition point. These studies resulted in constructing the microscopic
theory of liquid magnets, which took into account both liquid structure and Heisen-
berg exchange interaction responsible for ferromagnetism. Recently, this theory was
developed for the study of dynamical properties, and the explicit expressions for hy-
drodynamic time correlation functions were derived (I.M.Mryglod, M.V.Tokarchuk,
and Yu.K.Rudavskii).
In the papers by I.R.Yukhnovskii and Yu.V.Kozitskii, the collective variables
method was used in the studies of the critical behaviour of hierarchical models. These
studies found their development in works of Yu.V.Kozitskii on rigorous methods
in phase transition theory. The functional representation of the partition function
for cluster spin models was derived by I.R.Yukhnovskii and M.A.Korynevskii. This
allowed, using Yukhnovskii’s scheme, to calculate the free energy as well as other
thermodynamic functions for a cluster ferroelectric system (M.A.Korynevskii).
In the mid-80ties essential and principally new results were obtained by I.R.Yukh-
novskii in his studies of phase transitions in fluids. In cooperation with I.M.Idzyk
and V.O.Kolomiets he combined the reference system concept with the approach de-
veloped for the critical behaviour of the Ising model and constructed the microscopic
theory of the gas-liquid transition. In particular, it was found explicit expressions for
the chemical potential isotherm, a jump of density and the phase transition temper-
ature.The thermodynamic properties of a fluid both in one- and two-phase regions
were studied. In the papers by I.R.Yukhnovskii and O.V.Patsahan the statistical
theory of the fluid in the critical region was extended to the case of the classical
many-component mixtures. They used the collective variables method in conjunc-
tion with the reference system approach to describe the binary and many-component
mixtures near the gas-gas and fluid-fluid transition points.
The I.R.Yukhnovskii’s approach to a theoretical description of phase transitions
appeared to be very fruitful in its application to real physical objects, in particular, to
substitutional binary alloys. In the joint papers by I.R.Yukhnovskii and Z.O.Gurskii
the microscopic theory of thermodynamic properties of binary alloys was developed.
It was shown that the long-range order in alloys is connected with the atomic density
fluctuations that correspond to the absolute minimum of the ordering potential
Fourier transform. The equations for chemical potentials of the alloy components
were found and analysed. The free energy of the alloy as a function of temperature
and concentration and the equation of state were obtained. Thus, the collective
variables method yields a solution to the principle problem of the materials theory:
to predict physical properties of the alloy at different external parameters, e.g., the
temperature and the alloy composition.
In the mid-70th Professor Yukhnovskii initiated studies in the field of nonequi-
librium statistical theory. This was done in a close cooperation with Professor
D.N.Zubarev. On the basis of collective variables concept a new method in nonequi-
700
In honour of Professor Ihor Yukhnovskii. . .
librium theory of liquids, known as the generalized collective mode approach, was
formulated (I.M.Mryglod, M.V.Tokarchuk, I.P.Omelyan, and T.M.Bryk).
Statistical theory of partially excited systems which takes into consideration
the effective resonant interactions was developed in the works of I.R.Yukhnovskii,
R.R.Levitskii and O.V.Derzhko. On this basis the virial state equation and the
pair spatial distribution functions were obtained. In particular, the suggested theory
allowed one to explain the increase of critical temperature and pressure as well as the
change of the gas-liquid coexistence curve under the effect of resonance irradiation.
Since 1986 Ihor Yukhnovskii has been paying special attention to problems con-
nected with Chornobyl disaster. That year studies of aqueous solutions of radioactive
elements were started. The interest to the problem of interaction of fuel-containing
masses and fragments of reactor’s active zone with water and constructions’ materi-
als in the ”Shelter” site was initiated by I.Yukhnovskii and M.Tokarchuk. There were
performed the investigations which elucidated the role of radiolysis, hydrolysis and
creation of complexes in aqueous solutions of radioactive elements (uranyl, plutonyl
ions) that interact with fuel-containing masses. Prof. Yukhnovskii permanently em-
phasizes the active role of hydrogen in the processes of destruction of fuel-containing
masses interacting with aqueous solutions.
Professor Yukhnovskii pays much attention to other problems which are very
important to economy of Ukraine. In 1992 he was the first who initiated the devel-
opment of computer network facilities in Ukraine. At that time the first Ukrainian
network for research and educational institutions was created in Lviv (A.Ya.Saban
and I.A.Protsykevych). At present the problems of catalysis, optical methods of in-
formation protection, new technologies in energetics (fuel cells) are of great interest
to Professor Yukhnovskii.
Professor Yukhnovskii is the author of more than 500 papers and books. About
40 researchers under his supervision became Candidates of Sciences and 13 are
Doctors of Sciences. Yukhnovskii’s scientific and public contributions have been
recognized by many awards and honorary degrees. In 1982 he was elected Member
of the National Academy of Sciences of Ukraine, in 1986 he was awarded the Krylov
Prize of Ukrainian Academy of Sciences.
This overview of the scientific problems, in formulating and solving of which Prof.
Yukhnovskii participated, is far from being complete. At present he uses his scientific
and life experience in running Interbranch Analytical and Consultative Council of
Cabinet of Ministers of Ukraine that analyzes state of the Ukrainian economy, its
prospects and trends in its development.
The Editorial Board of “Condensed Matter Physics” congratulates Professor
Yukhnovskii on the occasion of his notable anniversary and acknowledges his unique
and valuable contribution to science in the world. We also express our grateful thanks
to all the authors of these two issues of CMP for their contributions.
701
In honour of Professor Ihor Yukhnovskii. . .
List of the main publications by Professor Ihor Yukhnovskii
1. Yukhnovskii I.R., Glauberman A.E. On the statistical theory of the concentrated
solutions of strong electrolytes. // Zhurn. Eksp. Teor. Fiz., 1952, vol. 22, p. 562–571
(in Russian).
2. Yukhnovskii I.R., Glauberman A.E. On the statistical theory of the concentrated
solutions of strong electrolytes. // Zhurn. Eksp. Teor. Fiz., 1952, vol. 22, p. 572–578
(in Russian).
3. Yukhnovskii I.R., Glauberman A.E. On the “superposition” approximation in the
theory of interacting particles systems. // Doklady AN SSSR, 1953, vol. 93, p. 999–
1002 (in Russian).
4. Yukhnovskii I.R. Binary distribution function for the systems of charged interacting
particles. I. // Zhurn. Eksp. Teor. Fiz., 1954, vol. 27, p. 690–698 (in Russian).
5. Yukhnovskii I.R. Application of collective variables and account of short range forces
in the theory of a system of charged particles. // Zhurn. Eksp. Teor. Fiz., 1958,
vol. 34, No. 2, p. 376–389 (in Russian).
6. Yukhnovskii I.R. On the statistical theory of ionic systems. // Ukr. Fiz. Zhurn., 1959,
vol. 4, No. 2, p. 167–176 (in Ukrainian).
7. Yukhnovskii I.R., Rakhimova I.S., Vladimirov V.V. On the theory of systems of
rarefied particles in an external field. // Ukr. Fiz. Zhurn., 1959, vol. 4, No. 3, p. 334–
344 (in Ukrainian).
8. Yukhnovskii I.R. Free energy for the systems of charged particles. // Doklady AN
SSSR, 1959, vol. 126, No. 3, p. 557–560 (in Russian).
9. Yukhnovskii I.R. On the statistical theory of mixed ion-dipole systems of interacting
particles. // Doklady AN SSSR, 1961, vol. 136, No. 6, p. 1317–1320 (in Russian).
10. Yukhnovskii I.R. Spatial distribution of particles in the method of collective variables.
// Ukr. Fiz. Zhurn., 1962, vol. 7, No. 3, p. 267–277 (in Ukrainian).
11. Yukhnovskii I.R., Nekrot A.A. Free energy and binary distribution functions of a
mixed ion-dipole system. // Ukr. Fiz. Zhurn., 1963, vol. 8, No. 6, p. 633–644 (in
Russian).
12. Yukhnovskii I.R. The quantum statistical sum and collective variables. II. Transition
function to collective variables. // Ukr. Fiz. Zhurn., 1964, vol. 9, No. 8, p. 827–838
(in Ukrainian).
13. Yukhnovskii I.R., Nekrot A.A. On some properties of binary distribution functions
of ions and dipole molecules. // Ukr. Fiz. Zhurn., 1964, vol. 9, No. 4, p. 365–374 (in
Ukrainian).
14. Yukhnovskii I.R. Statistical operator and collective variables. I. Displacement trans-
formation. // Ukr. Fiz. Zhurn., 1964, vol. 9, No. 7, p. 702–714 (in Ukrainian).
15. Yukhnovskii I.R., Hetzheim H. Theorie des quantenplasmas unter benutzung der
method der kollektiven variablen. // Wissenschaftliche Z. Univ. Rostok. Naturwiss-
eschaftliche Reihe, 1967, h. 7, p. 849–856 (in German).
16. Yukhnovskii I.R., Khettskheim Kh. On pseudopotential for quasiclassical plasma. //
Ukr. Fiz. Zhurn., 1968, vol. 13, No. 6, p. 881–889 (in Ukrainian).
17. Yukhnovskii I.R., Ostrovskii M.K. The properties of the transition functions to the
collective variables. // Bulletin of Lviv University, Ser. Physics, 1966, iss. 5(13),
p. 3–11 (in Ukrainian).
18. Yukhnovskii I.R. Some problems of modern state in the theory of charged parti-
702
In honour of Professor Ihor Yukhnovskii. . .
cle equilibrium systems. // Ukr. Fiz. Zhurn., 1969, vol. 14, No. 5, p. 705–719 (in
Ukrainian).
19. Yukhnovskii I.R., Golovko M.F. Statistic theory of equilibrium system of particles
with a complex electrostatic structure. I. Screening potential. // Ukr. Fiz. Zhurn.,
1969, vol. 14, No. 7, p. 1120–1129 (in Ukrainian).
20. Yukhnovskii I.R., Bigun G.I., Ahlbehrendt N. Investigation of electron gas in metals
by the displacement and collective variables method. I. Electron gas of high density.
// Ukr. Fiz. Zhurn., 1970, vol. 15, No. 7, p. 1142–1148 (in Ukrainian).
21. Yukhnovskii I.R., Ahlbehrendt N., Bigun G.I., Kelbg G. Investigation of electron gas
in metals by the displacement and collective variables method. II. Alkali metals. //
Ukr. Fiz. Zhurn., 1970, vol. 15, No. 7, p. 1149–1154 (in Ukrainian).
22. Yukhnovskii I.R., Ahlbehrendt N., Bigun G.I., Kelbg G. Das entartete electronengas
in der methode der kollektiven variablen. // Annal. Phys., 1970, vol. 24, No. 5/6,
p. 188–189 (in German).
23. Yukhnovskii I.R. Method of displacements and collective variables. Preprint of the
Institute for Theoret. Physics, ITP–71–26P, Kiev, 1971, 82 p. (in Russian).
24. Petrashko R.N., Yukhnovskii I.R. Binary distribution function of degenerate Fermi
systems. // Teor. Mat. Fiz., 1973, vol. 17, No. 1, p. 118–130 (in Russian).
25. Yukhnovskii I.R., Vysochanskii V.S., Golovko M.F. Binary distribution functions
of ion and dipole systems. // Ukr. Fiz. Zhurn., 1973, vol. 18, No. 1, p. 66–74 (in
Ukrainian).
26. Petrashko R.N., Yukhnovskii I.R. Study of pair correlation function of the degenerate
electron gas at small distances. // Teor. Mat. Fiz., 1973, vol. 17, No. 2, p. 250–262
(in Russian).
27. Yukhnovskii I.R. Separation of reference system in a collective variable method.
Preprint of the Institute for Theoretical Physics, ITP–74–149P, Kiev, 1974, 35 p.
(in Russian).
28. Yukhnovskii I.R., Rudavskii Yu.K. Application of the collective variable method to
the Ising model. I. Partition function. Preprint of the Institute for Theoret. Physics,
ITP–74–171P, Kiev, 1974, 34 p. (in Russian).
29. Yukhnovskii I.R., Petrashko R.N. On quantum virial decomposition for electron gas
in metals. // Ukr. Fiz. Zhurn., 1974, vol. 19, No. 6, p. 1039–1088 (in Ukrainian).
30. Yukhnovskii I.R. Statistical theory of equilibrium systems of charged particles. //
Adv. Plasma Physics, 1974, vol. 5, p. 51–67.
31. Yukhnovskii I.R., Rudavskii Yu.K. Application of the collective variable method to
the Ising model. II. Investigation of the behaviour of the pair correlation function
in the vicinity of the phase transition point. Preprint of the Institute for Theoret.
Physics, ITP–75–13P, Kiev, 1975, 18 p. (in Russian).
32. Yukhnovskii I.R. Integration of partition function of three-dimensional Ising model
in the collective variable method. Preprint of the Institute for Theoretical Physics,
ITP–76–24P, Kiev, 1976, 29 p. (in Russian).
33. Yukhnovskii I.R., Vakarchuk I.O. Properties of liquid He4 at low temperatures. //
Bulletin of the Acad. Sci. of UkrSSR, 1977, No. 9, p. 32–43 (in Ukrainian).
34. Yukhnovskii I.R. Integration of partition function of three-dimensional Ising model in
the collective variables method. I. // Ukr. Fiz. Zhurn., 1977, vol. 22, No. 2, p. 325–335
(in Ukrainian).
35. Yukhnovskii I.R. Integration of partition function of three-dimensional Ising model
703
In honour of Professor Ihor Yukhnovskii. . .
in the collective variables method. II. // Ukr. Fiz. Zhurn., 1977, vol. 22, No. 3,
p. 484–493 (in Ukrainian).
36. Yukhnovskii I.R., Kozlovskii M.P. Critical index for the correlation length in the Ising
three-dimensional model. // Doklady AN SSSR, 1977, vol. 236, No. 4, p. 846–849 (in
Russian).
37. Yukhnovskii I.R., Rudavskii Yu.K. Substantiation of the form of basis distribution
near the phase transition point in the Ising model. // Doklady AN SSSR, 1977,
vol. 236, No. 4, p. 579–582 (in Russian).
38. Yukhnovskii I.R., Rudavskii Yu.K. Behaviour of moments of Gaussian basis distribu-
tion of spin density fluctuations in pair correlation function of the Ising model near
critical point. // Ukr. Fiz. Zhurn., 1977, vol. 22, No. 2, p. 196–205 (in Ukrainian).
39. Yukhnovskii I.R., Rudavskii Yu.K. The collective variables representation for the
Ising model. // Ukr. Fiz. Zhurn., 1977, vol. 22, No. 1, p. 50–59 (in Ukrainian).
40. Yukhnovskii I.R. Distribution of the spin fluctuation waves of Ising model in the
region containing critical point. // Ukr. Fiz. Zhurn., 1977, vol. 22, No. 2, p. 315–324
(in Ukrainian).
41. Yukhnovskii I.R., Kozlovskii M.P. Recurrence relations in the three-dimensional Ising
model. // Ukr. Fiz. Zhurn., 1977, vol. 22, No. 7, p. 1126–1134 (in Ukrainian).
42. Yukhnovskii I.R. Partition function of the three-dimensional Ising model. // Doklady
AN SSSR, 1977, vol. 232, No. 2, p. 312–315 (in Russian).
43. Yukhnovskii I.R., Vakarchuk I.A. Application of the displacement and collective vari-
ables method for describing liquid helium near absolute zero. Preprint of the Institute
for Theoretical Physics, ITP–77–25E, Kiev, 1977, 67 p.
44. Yukhnovskii I.R. Partition function of the three-dimensional Ising model. // Teor.
Mat. Fiz., 1978, vol. 36, No. 3, p. 373–399 (in Russian).
45. Yukhnovskii I.R., Golovko M.F., Kuryljak I.I. Screening potential of limited ion-
dipole systems. // Ukr. Fiz. Zhurn., 1978, vol. 23, No. 6, p. 927–937 (in Russian).
46. Vakarchuk I.A., Yukhnovskii I.R. Self-consistent description of long- and short-range
correlations in the theory of liquid He4. I. // Theor. Math. Phys., 1979, vol. 40, No. 1,
p. 100–111.
47. Yukhnovskii I.R. Partition function of the three-dimensional Ising model. // Teor.
Mat. Fiz., 1978, vol. 36, No. 3, p. 373–399 (in Russian).
48. Honopolskii O.L., Vakarchuk I.A., Yukhnovskii I.R. Self-consistent description of
long- and short-range correlations in the theory of liquid He4. II. // Theor. Math.
Phys., 1979, vol. 41, No. 1, p. 77–88.
49. Yukhnovskii I.R., Holovko M.F. Statistical Theory of Classic Equilibrium Systems.
Kiev, Naukova Dumka, 1980 (in Russian).
50. Yukhnovskii I.R., Gruba V.D., Golovko M.F., Kessler Yu.M. Investigation of the
ion-ion mean force potential dependence on the parameters and form of ion-molecule
interaction potentials. // Ukr. Fiz. Zhurn., 1980, vol. 25, No. 10, p. 1611–1616 (in
Russian).
51. Vakarchuk I.A., Yukhnovskii I.R. Microscopic theory of liquid He4 energy spectrum.
// Theor. Math. Phys., 1980, vol. 42, No. 1, p. 112–123.
52. Yukhnovskii I.R., Holovko M.F., Kurylyak I.I., Sovyak E.M. Collective variables
method in the statistical theory of the bounded ion-molecular systems. // Fiz. Mol.,
1981, issue 10, p. 26–43 (in Russian).
53. Yukhnovskii I.R., Kozlovskii M.P., Kolomiets V.A. Investigation of the Ising three-
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In honour of Professor Ihor Yukhnovskii. . .
dimensional model by means of scale transformations. // Ukr. Fiz. Zhurn., 1982,
vol. 27, No. 6, p. 930–935 (in Russian).
54. Yukhnovskii I.R., Kozlovskii M.P., Kolomiets V.A. Analytical solution of equations
of a renormalization group. // Ukr. Fiz. Zhurn., 1982, vol. 27, No. 9, p. 1399–1403
(in Russian).
55. Kurylyak I.I., Yukhnovskii I.R. Collective variables method in equilibrium statistical
theory of bounded systems of charged particles. I. Continual model of electrolyte
solution in a half-space. // Teor. Mat. Fiz., 1982, vol. 52, No. 1, p. 114–126 (in
Russian).
56. Yukhnovskii I.R., Kozitskii Yu.V. Generalized hierarchical model of scalar ferromag-
net in the collective variable method. // Teor. Mat. Fiz., 1982, vol. 51, No. 2, p. 268–
277 (in Russian).
57. Vakarchuk I.A., Rudavskii Yu.K., Yukhnovskii I.R. Approximate renormalization
group transformation in the theory of phase transitions. I. Differential RG equation.
// Theor. Math. Phys., 1982, vol. 50, No. 2, p. 313–320.
58. Yukhnovskii I.R., Gurskii Z.A. Analysis of the first and second order phase transitions
in binary alloys by collective variables method. // Metal Physics, 1983, vol. 56, No. 4,
p. 672–681 (in Russian).
59. Yukhnovskii I.R., Kurylyak I.I., Kurylyak Ye.Ya. Studies of the surface layer struc-
ture in electrolyte solutions. // Physics of Many-Particle Systems, 1983, No. 3, p. 31–
35 (in Russian).
60. Yukhnovskii I.R. On the general theory of the second order phase transition. //
Physics of Many-Particle Systems, 1983, No. 4, p. 3–25 (in Russian).
61. Yukhnovskii I.R., Holovko M.F. Statistical theory of mixed ion-molecular systems.
Preprint of the Institute for Theoretical Physics, ITP-83–58E, Kiev, 1983, 62 p.
62. Mryglod I.M., Yukhnovskii I.R. The investigation of the approximate recurrent re-
lations of a n-component model for large values of division parameter s. Preprint of
the Institute for Theoretical Physics, ITP-84–181P, Kiev, 1984, 23 p. (in Russian).
63. Yukhnovskii I.R., Gurskii Z.A., Varanitskii V.I. Thermodynamical properties of alkali
metal alloys within the collective variables method. // Ukr. Fiz. Zhurn., 1984, vol. 29,
No. 9, p. 1389–1395 (in Russian).
64. Yukhnovskii I.R. Phase Transition of the Second Order. Collective Variables Method,
Kiev, Naukova Dumka, 1985, 252 p. (in Russian).
65. Yukhnovskii I.R., Patsagan O.V. Phase transitions in binary systems. The phase
space choice. Preprint of the Institute for Theoretical Physics, ITP–85–54P, Kiev,
1985, 24 p. (in Russian).
66. Yukhnovskii I.R., Holovko M.F. Approaches to the many-body theory of dense ion-
dipole plasma. // Chemical Physics of Solvation. Amsterdam, 1985, vol. A, p. 207–
262.
67. Yukhnovskii I.R., Kozlovskii M.P. Thermodynamic functions of the three-
dimensional Ising model at T > Tc. // Doklady Akad. Nauk UkrSSR, Ser. A, 1986,
No. 9, p. 62–65 (in Russian).
68. Yukhnovskii I.R. Description of the interaction in statistical physics. // Bulletin of
the Acad. Sci. of UkrSSR, 1986, No. 12, p. 6–18 (in Russian).
69. Yukhnovskii I.R. Phase Transitions of the Second Order: Collective Variables
Method. Singapore, World Scientific, 1987, 327 p.
70. Patsagan O.V., Yukhnovskii I.R. Phase transitions in two-component spatially ho-
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In honour of Professor Ihor Yukhnovskii. . .
mogeneous systems. I. The Gaussian approximation of the statistic sum functional.
// Teor. Mat. Fiz., 1987, vol. 72, No. 3, p. 452–461 (in Russian).
71. Idzyk I.M., Kolomiets V.A., Yukhnovskii I.R. Liquid-gas critical point in the col-
lective variables method. // Teor. Mat. Fiz., 1987, vol. 73, No. 2, p. 264–280 (in
Russian).
72. Yukhnovskii I.R., Vavrukh M.V. Many-body approach to the determination of the
energy spectrum of many-component superconductors. // Fiz. Niz. Temp., 1987,
vol. 13, No. 11, p. 1225–1229 (in Russian).
73. Yukhnovskii I.R., Rudavskii Yu.K., Holovatch Yu.V. Investigation of the critical be-
haviour of n-component Stanley model in the frames of collective variables method.
In: Thermodynamics of Irreversible Phenomena, Moscow, Nauka, 1987, p. 49–55 (in
Russian).
74. Yukhnovskii I.R., Gurskii Z.A., Chushak Ya.G. On contribution of atomic vibrations
to the binary alloy properties. // Fiz. Metall. Metalloved., 1987, vol. 63, No. 6,
p. 1089–1096 (in Russian).
75. Yukhnovskii I.R., Kolomiets V.A., Idzyk I.M. Free energy functional in the vicinity of
the liquid-vapour critical point. // Physics of Many-Particle Systems, 1988, vol. 14,
p. 18–24 (in Russian).
76. Yukhnovskii I.R., Korynevskii N.A. The investigation of the ferroelectric phase tran-
sition in cluster systems in the collective variables method. // Ukr. Fiz. Zhurn., 1988,
vol. 33, No. 12, p. 1832–1839 (in Russian).
77. Yukhnovskii I.R., Korynevskii N.A. The investigation of critical behaviour of uniaxial
cluster ferroelectrics. // Ferroelectrics Letters, 1988, No. 8, p. 117–120.
78. Yukhnovskii I.R., Kozlovskii M.P. The thermodynamics of the second-order phase
transition in the collective variables method. // Physics of Many-Particle Systems,
1988, vol. 14, p. 82–88 (in Russian).
79. Yukhnovskii I.R., Kurylyak I.I. Electrolytes, Kiev, Naukova Dumka, 1988, 168 p. (in
Russian).
80. Patsagan O.V., Yukhnovskii I.R. Thermodynamical functions of double component
space homogeneous system in the vicinity of critical separation point. // Teor. Mat.
Fiz., 1989, vol. 81, No. 3, p. 455–467 (in Russian).
81. Yukhnovskii I.R., Kadobyanskii R.N., Levitskii R.R., Derzhko O.V. Effective inter-
actions in groups of identical particles containing excited ones. // Ukr. Fiz. Zhurn.,
1989, vol. 34, No. 2, p. 300–307 (in Russian).
82. Yukhnovskii I.R., Kozlovskii M.P., Ilnytskii Ya.N. On the choice of renormalization
group parameter under the studying of the 3d Ising model. // Ukr. Fiz. Zhurn., 1989,
vol. 34, No. 7, p. 1106–1100 (in Russian).
83. Yukhnovskii I.R., Levitskii R.R., Derzhko O.V. Resonance irradiation influence on
the gas-liquid phase transition. // Physics Letters A, 1989, vol. 141, No. 1–2, p. 18–
24.
84. Yukhnovskii I.R., Korynevskii N.A. The investigation of the ferroelectric phase tran-
sition in cluster systems of order-disorder type. I. Partition function functional. //
Phys. Stat. Sol. (b), 1989, vol. 153, p. 583–593.
85. Yukhnovs’kii I.R. Solution of the three-dimensional Ising model of the second-order
phase transition. // La Rivista del Nuovo Cimento, 1989, vol. 12, No. 1, p. 1–119.
86. Patsagan O.V., Yukhnovskii I.R. Grand statistical sum functional in the collective
variables method with a distinguished reference system. Multicomponent system. //
706
In honour of Professor Ihor Yukhnovskii. . .
Teor. Mat. Fiz., 1990, vol. 83, No. 1, p. 72–82 (in Russian).
87. Yukhnovskii I.R. The functional of the grand partition function for the investigation
of the liquid-gas critical point. // Physica A, 1990, vol. 168, No. 3, p. 999–1020.
88. Yukhnovskii I.R., Gurskii Z.A. Quantum-Statistical Theory of Disordered Systems.
// Kyiv, Naukova Dumka, 1991 (in Russian).
89. Kozlovskii M.P., Pylyuk I.V., Yukhnovskii I.R. Thermodynamic functions of three-
dimensional Ising model near the phase transition point with allowance for corrections
to scaling. // Theor. Math. Phys., 1991, vol. 87, No. 2, p. 540–556.
90. Kozlovskii M.P., Pylyuk I.V., Yukhnovskii I.R. Thermodynamic functions of three-
dimensional Ising model near the phase transition point with allowance for corrections
to scaling. II. The case T<Tc. // Theor. Math. Phys., 1991, vol. 87, No. 3, p. 641–656.
91. Yukhnovskii I.R., Kozlovskii M.P., Pylyuk I.V. A method for the calculation of ther-
modynamic functions for the 3D model systems in the critical region. // Z. Natur-
forsch, 1991, vol. 46a, p. 1–7.
92. Yukhnovskii I.R., Gurskii Z.O., Chushak Ya.G. Calculation of the free energy and
the pair correlation functions of disordered binary alloys by the method of collective
variables. // Phys. Stat. Sol. (b), 1991, vol. 163, No. 1, p. 107–118.
93. Yukhnovskii I.R., Korinevskii N.A. The investigation of the ferroelectric phase tran-
sition in cluster system of order-disorder type. III. Free energy. // Phys. Stat. Sol.
(b), 1991, vol. 163, No. 1, p. 333–367.
94. Yukhnovskii I.R., Levitskii R.R., Sorokov S.I., Derzhko O.V. Theory of quasispin
systems described by a quasi-one-dimensional Ising model in transverse field, with
the short-range interactions taken into account in a reference approach. // Izv. AN
SSSR, 1991,vol. 55, No. 3, p. 481–490 (in Russian).
95. Yukhnovskii I.R., Levitskii R.R., Sorokov S.I. The study of quasispin systems in
reference system approach. // Cond. Matt. Phys., 1993, No. 1, p. 43–62.
96. Yukhnovskii I.R., Derzhko O.V., Levitskii R.R. Cluster expansion method in the
theory of equilibrium properties of a gas of atoms of which a part is excited. //
Physica A, 1994, vol. 203, Nos. 3–4, p. 381–413.
97. Yukhnovskii I.R., Tokarchuk M.V., Omelyan I.P., Zhelem R.I. Statistical theory for
diffusion of radionuclides in ground and underground water. I. Statistical model.
Preprint of the Institute for Condensed Matter Physics, ICMP-94–7E, Lviv, 1994,
19 p.
98. Yukhnovskii I.R., Kolomiets V.A., Idzyk I.M. Application of the collective variable
method used the separate reference system to description of a real system like Ar
in the region T>Tc. // Ukr. Fiz. Zhurn., 1995, vol. 40, Nos. 1/2, p. 123–128 (in
Ukrainian).
99. Yukhnovskii I.R., Kozlovskii M.P. Description of the phase transition in 3D systems.
// JMMM, 1995, vol. 140–144, p. 1477–1478.
100. Yukhnovskii I.R., Idzyk I.M., Kolomiets V.O. Investigation of a homogeneous many-
particle system in the vicinity of the critical point. // J. Stat. Phys., 1995, vol. 80,
Nos. 1/2, p. 405–443.
101. Yukhnovskii I.R., Patsahan O.V. Grand canonical distribution for multicomponent
system in the collective variables method. // J. Stat. Phys., 1995, vol. 81, Nos. 3/4,
p. 647–672.
102. Ilnytskyi Ya.M., Kozlovskii M.P., Yukhnovskii I.R. On the theory of phase transitions
by collective variables method. // Int. Journ. of Mod. Phys. B., 1997, vol. 11, No. 8,
707
In honour of Professor Ihor Yukhnovskii. . .
p. 1009–1022.
103. Kozlovskii M.P., Yukhnovskii I.R. Method for the self-consistent description of the
critical behaviour of the three-dimensional Ising-like system at a microscopic level.
Preprint of the Institute for Condensed Matter Physics, ICMP–97–25U, Lviv, 1997,
96 p.
104. Yukhnovskii I.R., Kobryn O.E., Tokarevskii V.V., Tokarchuk M.V. Problems on in-
teraction between water and fuel containing masses inside the object “Shelter” of
Chornobyl Nuclear Power Plant. // J. Phys. Studies, 1997, vol. 1, No. 2, p. 169–180.
105. Yukhnovskii I.R., Tokarchuk M.V., Ignatyuk V.V., Kobryn A.E., Omelyan I.P.,
Zhelem R.I., Dmytriv G.S., Ivankiv O.L. Studies on nonequilibrium physico-chemical
processes in a system “fuel containing masses - aqueous solutions of radioactive ele-
ments”. // Cond. Matt. Phys., 1997, No. 12, p. 63–96.
106. Yukhnovskii I.R., Tokarchuk M.V., Kobryn O.E., Dmytriv G.S., Humenyuk Y.A.
Analysis of chemical reactions of radiolysis, hydrolysis and complex formation in
alkali solutions of the object “Shelter”. // J. Phys. Studies, 1999, vol. 3, No. 2,
p. 224–236.
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