ISING MODELS WITH SPIN 1
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]/a>, 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].
References:
[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.
