Ostap Baran

Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine
Spin-1 Ising model with higher-degree spin terms (of an exchange as well as of a non-exchange origin) in the Hamiltonian is one of the most extensively studied models in condensed matter physics. That is so not only because of the fundamental theoretical interest arising from the richness of the phase diagram that is exhibited due to competition of interactions, but also because versions and extensions of this model can be applied for the description of simple and multi-component fluids [1-3], dipolar and quadrupolar orderings in magnets [3-5], crystals with ferromagnetic impurities [3], ordering in semiconducting alloys [6], etc. Ising model with S=1 has been investigated by different simulation and approximate techniques: using the mean-field approximation [1-4,7], effective field theory [8,9], two-particle cluster approximation [10,11], Bethe approximation [12], high-temperature series expansions [13], renormalization-group theory [14, 15], and Monte-Carlo simulations [12,16,17].
[1] D. Mukamel, M. Blume. Ising model for tricritical points in ternary mixtures. Phys. Rev. A, 10 (1974) 610.
[2] D. Furman, S. Dattagupta, R.B. Griffiths. Global phase diagram for a three-component model. Phys. Rev. B, 15 (1977) 441.
[3] J. Sivardiere. In: Proc. Internat. Conf. Static critical phenomena in inhomogeneous systems, Karpacz 1984, Lecture notes in physics, 206, Springer-Verlag, Berlin 1984.
[4] H.H. Chen, P.M. Levy. Dipole and quadrupole phase transitions in spin-1 models. Phys. Rev. B, 7 (1973) 4267.
[5] E.L. Nagaev. Magnetics with complicated exchange interaction. Izd. Nauka, Moscow, 1988.
[6] K.E. Newman, J.D. Dow. Zinc-blende-diamond order-disorder transition in metastable crystalline (GaAs)1-xGe2x alloys. Phys. Rev. B, 27 (1983) 7495.
[7] W. Hoston, A.N. Berker. Multicritical phase diagrams of the Blume-Emery-Griffiths model with repulsive biquadratic coupling. Phys. Rev. Lett. 67 (1991) 1027.
[8] T. Kaneyoshi, E.F. Sarmento. The application of the differential operator method to the Blume-Emery-Griffiths model. Physica A, 152 (1988) 343.
[9] J.W. Tucker. Two-site cluster theory for the spin-one Ising model. J. Magn. Magn. Mat. 87 (1990) 16.
[10] S.I. Sorokov, R.R. Levitskii, O.R. Baran. Investigation of an Ising-type Model with an arbitrary value of spin within the two-particle cluster approximation. Blume-Emery-Griffiths Model. Ukr. Fiz. Zhurn. 41 (1996) 490.
[11] S.I. Sorokov, R.R. Levitskii, O.R. Baran. Two-particle cluster approximation for Ising type model with arbitrary value of spin. Correlation functions of Blume-Emery-Griffiths model. Cond. Matt. Phys. 9 (1997) 57.
[12] K. Kasono, I. Ono. Re-entrant phase transitions of the Blume-Emery-Griffiths model. Z. Phys. B, 88 (1992) 205.
[13] D. Saul, M. Wortis, D. Stauffer. Tricritical behavior of the Blume-Capel model. Phys. Rev. B, 9 (1974) 4964.
[14] A. Bakchick, A.Benyoussef, M. Touzani. Phase diagrams of the Blume-Emery-Griffiths model: real-space renormalization group investigation and finite size scaling analysis. Physica A, 186 (1992) 524.
[15] R.R. Netz, A.N. Berker. Renormalization-group theory of an internal critical-end-point structure: The Blume-Emery-Griffiths model with biquadratic repulsion. Phys. Rev. B, 47 (1993) 15019.
[16] O.F. De Alcantara Bonfim, C.H. Obcemea. Reentrant behaviour in Ising models with biquadratic exchange interaction. J. Phys. B, 64 (1986) 469.
[17] D. Pena Lara, J.A. Plascak. The critical behavior of the general spin Blume–Capel model. Int. J. Mod. Phys. B, 12 (1998) 2045.
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