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Current issue    Ukr. J. Phys. 2015, Vol. 60, N 4, p.362-370
https://doi.org/10.15407/ujpe60.04.0362    Paper

Kozlovskii M.P., Pylyuk I.V.

Institute for Condensed Matter Physics, Nat. Acad. of Sci. of Ukraine
(1, Svientsitskii Str., Lviv 79011, Ukraine; e-mail: piv@icmp.lviv.ua)

Analytical Description of the Critical Behavior of a Three-Dimensional Uniaxial Magnet in an External Field by Singling out a Reference System

Section: General problems of theoretical physics
Language: Ukrainian

Abstract: The critical behavior of systems belonging to the universality class of the three-dimensional Ising model has been studied theoretically. A three-dimensional Ising-like system with exponentially decreasing interaction potential and in the presence of a homogeneous external field was considered in the framework of the collective variables method. A specific feature in the calculation of the partition function and the free energy of a uniaxial magnet consists in singling out a reference system. The role of the latter is played by the molecular-field Hamiltonian. A method to describe the critical behavior with the use of a singled out reference system is developed on the basis of a non-Gaussian (quartic) distribution of order-parameter fluctuations (the 4 model).

Key words: Ising model, critical behavior, reference system, non-Gaussian distributions, free energy.


  1. I.R. Yukhnovskii, Preprint ITF-88-30R (Institute for Theoretical Physics, Kiev, 1988) (in Russian).
  2. I.R. Yukhnovskii, Phase Transitions of the Second Order. Collective Variables Method (World Scientific, Singapore, 1987). CrossRef
  3. I.R. Yukhnovskii, M.P. Kozlovskii, and I.V. Pylyuk, Ukr. Fiz. Zh. 57, 83 (2012).
  4. R.J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic Press, London, 1982).
  5. A.K. Zvezdin, V.M. Matveev, A.A. Mukhin, and A.A. Popov, Rare-Earth Ions in Magnetically Ordered Crystals (Nauka, Moscow, 1985) (in Russian).
  6. W.P. Wolf, Braz. J. Phys. 30, 794 (2000). CrossRef
  7. W.L. Bragg and E.J. Williams, Proc. Roy. Soc. A 145, 699 (1934). CrossRef
  8. M.P. Kozlovskii, Ukr. Fiz. Zh. (Oglyady) 5, 61 (2009).
  9. I.R. Yukhnovskii, M.P. Kozlovskii, and I.V. Pylyuk, Phys. Rev. B 66, 134410 (2002). CrossRef
  10. I.R. Yukhnovskii, M.P. Kozlovskii, and I.V. Pylyuk, Microscopic Theory of Phase Transitions in the Three-Dimensional Systems (Eurosvit, Lviv, 2001) (in Ukrainian).
  11. I.R. Yukhnovskii, Physica A 168, 999 (1990). CrossRef
  12. I.R. Yukhnovskii, I.M. Idzyk, and V.O. Kolomiets, J. Stat. Phys. 80, 405 (1995). CrossRef
  13. I.R. Yukhnovskii, Condens. Matter Phys. 17, 43001 (2014). CrossRef
  14. M.P. Kozlovskii and O.V. Patsahan, Condens. Matter Phys. 3, 607 (2000). CrossRef