
ISING MODELS WITH SPIN 1Ostap BaranInstitute for Condensed Matter Physics, National Academy of Sciences of UkraineSpin1 Ising model with higherdegree spin terms (of an exchange as well as of a nonexchange 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 multicomponent fluids [13], dipolar and quadrupolar orderings in magnets [35], 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 meanfield approximation [14,7], effective field theory [8,9], twoparticle cluster approximation [10,11], Bethe approximation [12], hightemperature series expansions [13], renormalizationgroup theory [14, 15], and MonteCarlo 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 threecomponent 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, SpringerVerlag, Berlin 1984. [4] H.H. Chen, P.M. Levy. Dipole and quadrupole phase transitions in spin1 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. Zincblendediamond orderdisorder transition in metastable crystalline (GaAs)_{1x}Ge_{2x} alloys. Phys. Rev. B, 27 (1983) 7495. [7] W. Hoston, A.N. Berker. Multicritical phase diagrams of the BlumeEmeryGriffiths 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 BlumeEmeryGriffiths model. Physica A, 152 (1988) 343. [9] J.W. Tucker. Twosite cluster theory for the spinone Ising model. J. Magn. Magn. Mat. 87 (1990) 16. [10] S.I. Sorokov, R.R. Levitskii, O.R. Baran. Investigation of an Isingtype Model with an arbitrary value of spin within the twoparticle cluster approximation. BlumeEmeryGriffiths Model. Ukr. Fiz. Zhurn. 41 (1996) 490. [11] S.I. Sorokov, R.R. Levitskii, O.R. Baran. Twoparticle cluster approximation for Ising type model with arbitrary value of spin. Correlation functions of BlumeEmeryGriffiths model. Cond. Matt. Phys. 9 (1997) 57. [12] K. Kasono, I. Ono. Reentrant phase transitions of the BlumeEmeryGriffiths model. Z. Phys. B, 88 (1992) 205. [13] D. Saul, M. Wortis, D. Stauffer. Tricritical behavior of the BlumeCapel model. Phys. Rev. B, 9 (1974) 4964. [14] A. Bakchick, A.Benyoussef, M. Touzani. Phase diagrams of the BlumeEmeryGriffiths model: realspace renormalization group investigation and finite size scaling analysis. Physica A, 186 (1992) 524. [15] R.R. Netz, A.N. Berker. Renormalizationgroup theory of an internal criticalendpoint structure: The BlumeEmeryGriffiths 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. Personal webpage 