References
L. D. Landau:JETP,7, 19, (1937); 627 (1937).
J. D. Van-der-Waals: Ph. D. Thesis, University of Leiden (1973).
F. Weiss:J. Phys. Rad.,6, 667 (1907).
R. Braut:Phase Transitions (Mir, Moscow, 1967) (in Russian);R. Braut:Phase Transitions (Benjamin, New York, N.Y. 1965).
L. D. Landau andE. M. Lifshitz:Statistical Physics (Oxford, Pergamon Press, 1958).
E. Stanley:Introduction to phase transitions and critical phenomena (Clarendon Oxford, Press, 1971; Mir Moscow, 1974).
D. Jasnow andM. Wortis:Phys. Rev.,176, 739 (1968).
L. Onsager:Phys. Rev.,65, 117 (1944).
N. N. Bogolubov:Selected Papers, Vol.3 (Naukova Dumka, Kiev, 1971) (in Russian).
P. Hohenberg:Phys. Rev.,158, 383 (1967).
N. Mermin andH. Wagner:Phys. Rev. Lett,17, 1133 (1966).
E. C. G. Stueckelberg andA. Petermann:Helv. Phys. Acta,25, 499, (1953).
M. Gell-Mann andF. E. Low:Phys. Rev.,95, 1300 (1954).
N. N. Bogolubov andD. V. Shirkov:JETP,30, 77 (1956) (in Russian).
N. N. Bogolubov and D. V. Shirkov:Introduction to Quantum Field Theory (Nauka, Moscow, 1976) (in Russian).
B. Widom:J. Chem. Phys.,43, 3898 (1965).
A. Z. Patashinskii andV. A. Pokrovskii:JETP,50, 439 (1966) (in Russian).
A. Z. Patashinskii and V. A. Pokrovskii:Fluctuation Theory of Phase Transitions (Nauka, Moscow, 1975), p. 380 (in Russian).
L. P. Kadanoff:Physics, Vol.2 (New York, N.Y., 1966), p. 263.
P. W. Anderson:J. Phys. C,3, 2436 (1970).
C. Dicastro andG. Lazinio:Phys. Lett. A,29, 322 (1969).
K. Wilson andJ. Kogut:Phys. Rep. C,12, 75 (1974).
K. G. Wilson:Phys. Rev. B,4, 3174 (1971).
S. K. Ma:Modern Theory of Critical Phenomena (Benjamin, New York, N.Y., 1976).
H. J. Hillhorst andJ. M. J. van Leewen:Physica, (Utrecht) A,106, 301 (1981).
L. P. Kadanoff andA. Houghton:Phys. Rev. B,11, 377 (1975).
J. M. J. van Leewen:Phys. Rev. Lett.,34, 1056 (1975).
Th. Niemeyer andJ. M. J. van Leewen:Physica,71, 17 (1974).
L. Sneddon andM. N. Barber:J. Phys. C,10, 2653 (1977).
F. J. Wegner andA. Houghton:Phys. Rev. A,8, 401 (1973).
L. P. Kadanoff:Phys. Rev. Lett.,34, 1005 (1975).
R. H. Swendsen:Phys. Rev. Lett.,43, 177 (1979).
K. G. Wilson:Phys. Rev. D,7, 2911 (1973).
K. G. Wilson andM. E. Fisher:Phys. Rev. Lett.,28, 240 (1972).
B. Widom:Mol. Phys.,25, 657 (1973).
D. E. Khmelnitskii:JETP,68, 1960 (1975).
F. J. Dyson:Commun. Math. Phys.,12, 91 (1969).
Y. G. Sinai:Phase Transitions. Rigorous Results (Nauka, Moscow, 1980) p. 207 (in Russian).
D. N. Zubarev:Dokl. AN SSSR,95, 757 (1954) (in Russian).
I. R. Yukhnovs’kii:JETP,34, 379 (1958) (in Russian).
Y. V. Kozitskii:Application of collective variables method to the investigation of scalar models of phase transitions, Thesis (Kiev, 1981), p. 130 (in Russian).
I. R. Yukhnovs’kii and M. F. Holovko:Statistical Theory of Classical Equilibrium Systems (Naukova Dumka, Kiev, 1980), p.372.
I. R. Yukhnovs’kii andY. K. Rudavskii:Ukr. Fiz. J.,22, 50 (1977);Dokl. AN SSR 233, 579 (1977) (in Russian).
I. R. Yukhnovs’kii and Y. K. Rudavskii: Preprint Inst. Theor. Phys. Acad. Sci. Ukr. SSR, ITP-74-171R (1974); ITP-75-13R (1975) (in Russian).
I. R. Yukhnovs’kii: Preprint Inst. Theor. Phys. Acad. Sci. Ukr. SSR, ITP-76-15R (1976) (in Russian).
I. R. Yukhnovs’kii:Dokl. AN SSSR,232, 312 (1977).
V. A. Kolomiets:numerical calculations of three-dimensional Ising model in the collective variables method Thesis (Lvov, 1982), p. 161 (in Russian).
Y. K. Rudavskii:Investigation of Ising model by the collective variables method, Thesis (Lvov, 1976), p. 115 (in Russian).
F. Dyson, E. Montroll, T. Katz and M. Fisher:Stability and Phase Transitions (Mir, Moscow, 1973), p. 369 (in Russian).
J. A. Vakarchuk andY. K. Rudavskii:Theor. Math. Phys.,50, 313 (1982) (in Russian).
J. A. Vakarchuk andY. K. Rudavskii:Theor. Math. Phys.,51, 102 (1982) (in Russian).
Y. V. Kozitskii andI. R. Yukhnovs’kii:Theor. Math. Phys.,51, 268 (1982) (in Russian).
V. N. Popov:Continual Integrals in Quantum Field Theory and Statistical Physics (Atomizdat, Moscow, 1976), p. 256 (in Russian).
V. L. Ginzburg andL. D. Landau:JETP,20, 1064 (1950).
I. R. Yukhnovs’kii:Ukr. Phys. J.,22, 315 (1977) (in Russian).
I. R. Yukhnovs’kii:Theor. Math. Phys.,36, 273 (1978 (in Russian).
Handbook of Mathematical Functions with Formulae Graphs and Mathematical Table, edited byM. Abramowitz and I. Stegun (Nauka, Moscow, 1979) (in Russian).
I. S. Grandstein and I. I. Ryzhyk:Tables of Integrals, Sums, Series and Products (Moscow, Nauka, 1971), p. 1108 (in Russian).
I. R. Yukhnovs’kii:Ukr. Phys. J.,22, 325, 484 (1977) (in Russian).
I. R. Yukhnovs’kii andM. P. Kozlovskii:Ukr. Phys. J.,22, 1125 (1977); Preprint Inst. Theor. Phys. Acad. Sci. Ukr. SSR, ITP-78-128R (1978) (in Russian).
M. P. Kozlovskii: Preprint Inst. Theor. Phys. Acad. Sci. Ukr. SSR, ITP-81-82R (1981); JTP-82-80R (1982) (in Russian).
M. P. Kozlovskii: Preprint Inst. Theor. Phys. Acad. Sci. Ukr. SSR, ITP-82-104 (1982);Behaviour of thermodynamic functions near the phase transition point of the Ising model, Thesis, (Kiev, 1977), p. 144;Physics of Many-Particle Systems, Vol.4, (Naukova Dumka, Kiev, 1983), p. 37 (in Russian).
I. R. Yukhnovs’kii, M. P. Kozlovskii and Kolomiets: Preprint Inst. Theor. Phys. Acad. Sci. Ukr. SSR, ITP-80-3R (1980); ITP-80-111R (1980) (in Russian).
I. R. Yukhnovs’kii, M. P. Kozlovskii and V. A. Kolomiets: Preprint Inst. Theor. Phys. Acad. Sci. Ukr. SSR, ITP-81-47R (1981); ITP-81-48R (1981);Ukr. Phys. J.,27, 925, 1399 (1982) (in Russian).
I. R. Yukhnovs’kii:Physics of Many-Particle Systems, Vol.4, (Naukova Kiev Dumka, 1983), p. 3.
I. R. Yukhnovs’kii: Preprint Inst. Theor. Phys. Acad. Sci. Ukr. SSR, ITP-83-6E (1983), ITP-83-85E (1983).
I. R. Yukhnovs’kii, M. P. Kozlovskii and N. A. Shpot: Preprint Inst. Theor. Phys. Acad. Sci. Ukr. SSR, ITP-84-144E (1984).
Kozlovsky M. P. and Pylyuk I. V.: Preprint ITP-85-23E.
M. P. Kozlovsky, I. M. Ilnitsky and I. V. Pylyuk: Preprint ITP-85-107R.
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Yukhnovs’kii, I.R. Solution of the three-dimensional Ising model for description of the second-order phase transition. Riv. Nuovo Cim. 12, 1–119 (1989). https://doi.org/10.1007/BF02740597
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DOI: https://doi.org/10.1007/BF02740597