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

  • M. P. Kozlovskii Institute for Condensed Matter Physics, Nat. Acad. of Sci. of Ukraine
  • I. V. Pylyuk Institute for Condensed Matter Physics, Nat. Acad. of Sci. of Ukraine
Keywords: Ising model, critical behavior, reference system, non-Gaussian distributions, free energy

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 p4 model).

References

I.R. Yukhnovskii, Preprint ITF-88-30R (Institute for Theoretical Physics, Kiev, 1988) (in Russian).

I.R. Yukhnovskii, Phase Transitions of the Second Order. Collective Variables Method (World Scientific, Singapore, 1987).

http://dx.doi.org/10.1142/0289

I.R. Yukhnovskii, M.P. Kozlovskii, and I.V. Pylyuk, Ukr. Fiz. Zh. 57, 83 (2012).

R.J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic Press, London, 1982).

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).

W.P. Wolf, Braz. J. Phys. 30, 794 (2000).

http://dx.doi.org/10.1590/S0103-97332000000400030

W.L. Bragg and E.J. Williams, Proc. Roy. Soc. A 145, 699 (1934).

http://dx.doi.org/10.1098/rspa.1934.0132

M.P. Kozlovskii, Ukr. Fiz. Zh. (Oglyady) 5, 61 (2009).

I.R. Yukhnovskii, M.P. Kozlovskii, and I.V. Pylyuk, Phys. Rev. B 66, 134410 (2002).

http://dx.doi.org/10.1103/PhysRevB.66.134410

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).

I.R. Yukhnovskii, Physica A 168, 999 (1990).

http://dx.doi.org/10.1016/0378-4371(90)90268-W

I.R. Yukhnovskii, I.M. Idzyk, and V.O. Kolomiets, J. Stat. Phys. 80, 405 (1995).

http://dx.doi.org/10.1007/BF02178366

I.R. Yukhnovskii, Condens. Matter Phys. 17, 43001 (2014).

http://dx.doi.org/10.5488/CMP.17.43001

M.P. Kozlovskii and O.V. Patsahan, Condens. Matter Phys. 3, 607 (2000).

http://dx.doi.org/10.5488/CMP.3.3.607

Published
2019-01-19
How to Cite
Kozlovskii, M., & Pylyuk, I. (2019). Analytical Description of the Critical Behavior of a Three-Dimensional Uniaxial Magnet in an External Field by Singling Out a Reference System. Ukrainian Journal of Physics, 60(4), 362. https://doi.org/10.15407/ujpe60.04.0362
Section
General problems of theoretical physics