Mixed Spin-2 and Spin-3/2 Blume-Emery-Griffiths (BEG) Model on the Bethe Lattice


The mixed spin-2 and spin-3/2 Blume-Emery-Griffiths (BEG) Ising ferrimagnetic system is studied by the Bethe lattice approach. The ground-state phase diagram is constructed. The influence of the crystal-field and the biquadratic interactions among neighboring spins on the thermal behaviors of the system is singled out. The system displays very rich critical behaviors with the existence of tricritical points. Compensation points where the global magnetization of the system vanishes have been detected for appropriate values of the system parameters.

Share and Cite:

Karimou, M. , Yessoufou, R. and Hontinfinde, F. (2015) Mixed Spin-2 and Spin-3/2 Blume-Emery-Griffiths (BEG) Model on the Bethe Lattice. World Journal of Condensed Matter Physics, 5, 187-200. doi: 10.4236/wjcmp.2015.53020.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Khan, O. (1993) Molecular Magnetism. VCH, New York.
[2] Monsuripur, M. J. (1987) Magnetization Reversal, Coercivity, and the Process of Thermomagnetic Recording in Thin Films of Amorphous Rare Earth-Transition Metal Alloys. Journal of Applied Physics, 61, 1580. http://dx.doi.org/10.1063/1.338094
[3] Gatteshi, D., Khan, O., Miller, J.S. and Palacio, F., Eds. (1991) Magnetic Molecular Materials, NATO ASI Series. Kluwer Academic, Dordrecht.
[4] Benayad, N. and Zittartz, J.Z. (1990) Real-Space Renormalization Group Investigation of the Three-Dimensional Semi-Infinite Mixed Spin Ising Model. Zeitschrift für Physik B Condensed Matter, 81, 107-112. http://dx.doi.org/10.1007/BF01454221
[5] Yousif, B.Y. and Bowers, R.G. (1984) High-Temperature Series Expansion Studies of Mixed Spin-1/2-Spin-S Ising Models. Journal of Physics A: Mathematical and General, 17, 3389.
[6] Tang, F.K. (1988) Critical Couplings of Mixed Spin-1/2-Spin-S Isingmodel: A Free-Fermion Approximation. Journal of Physics A: Mathematical and General, 21, L1097.
[7] Ekiz, C. (2006) Effect of Crystal-Field Potential on Compensation Temperature of a Mixed Spin-1/2 and Spin-1 Ising Ferrimagnetic System. Physics Letters A, 352, 291-295.
[8] Iwashi, T. and Uryu, N. (1983) The Effect of the Biquadratic Exchange Interaction on the Curie Temperature of the Mixed Ising Ferromagnet. Physics Letters A, 96, 311-313.
[9] Zhang, G.M. and Yang, C.Z. (1993) Monte Carlo Study of the Two-Dimensional Quadratic Ising Ferromagnet with Spins S = 1/2 and S = 1 and with Crystal-Field Interactions. Physical Review B, 48, 9452. http://dx.doi.org/10.1103/PhysRevB.48.9452
[10] Buendia, G.M. and Novotny, M.A. (1997) Numerical Study of a Mixed Ising Ferrimagnetic System. Journal of Physics: Condensed Matter, 9, 5951. http://dx.doi.org/10.1088/0953-8984/9/27/021
[11] Tucker, J.W. (1999) The Ferrimagnetic Mixed Spin 1/2 and Spin 1 Ising System. Materials, 195, 733-740. http://dx.doi.org/10.1016/S0304-8853(99)00302-9
[12] Bobák, A. (1988) An Effective-Field Theory of Mixed Ising Spin Systems in Transverse Fields. Physica Status Solidi B, 150, 261-272. http://dx.doi.org/10.1002/pssb.2221500129
[13] Bobák, A., Abubrig, O.F., Horvath, D. and Jascur, M. (2001) Mean-Field Solution of the Mixed Spin-1 and Spin-3/2 Ising System with Different Single-Ion Anisotropies. Physica A: Statistical Mechanics and Its Applications, 296, 437-450. http://dx.doi.org/10.1016/S0378-4371(01)00176-5
[14] Albayrak, E. (2008) Mixed Spin-1 and Spin-3/2 Blume-Capel Ising Ferrimagnetic System on the Bethe Lattice. International Journal of Modern Physics B, 17, 1087-1100.
[15] Ekiz, C. and Magn, J. (2006) The Possibility of Two Compensation Points in a Ferrimagnetic Mixed Spin-1 and Spin-3/2 Ising System Using Bethe Lattice Approach. Journal of Magnetism and Magnetic Materials, 307, 139-147. http://dx.doi.org/10.1016/j.jmmm.2006.03.059
[16] Yessoufou, R.A., Kpadonou, V.A. and Hontinfinde, F. (2011) Mixed Spin-1 and Spin-3/2 B C Ferromagnetic System on the Two-Fold Cayley Tree. The African Review of Physics, 6, 203-210.
[17] Albayrak, E. (2007) Mixed Spin-2 and Spin-5/2 Blume-Emery-Griffiths Model. Physica A: Statistical Mechanics and its Applications, 375, 174-184. http://dx.doi.org/10.1016/j.physa.2006.08.054
[18] Deviren, B., Kantar, E. and Keskin, M. (2010) Magnetic Properties of a Mixed Spin-3/2 and Spin-2 Ising Ferrimagnetic System within the Effective-Field Theory. Journal of the Korean Physical Society, 56, 1738-1747. http://dx.doi.org/10.3938/jkps.56.1738
[19] Abubrig, F. (2013) Magnetic Properties of a Mixed-Spin-3/2 and Spin-2 Ising Ferrimagnetic System in an Applied Longitudinal Magnetic Field. World Journal of Condensed Matter Physics, 3, 111-118.
[20] Kurota, M., Kikuchi, R. and Watari, T. (1953) A Theory of Cooperative Phenomena. III. Detailed Discussions of the Cluster Variation Method. The Journal of Chemical Physics, 21, 434.
[21] Hu, C.-K. and Izmailian, N.S. (1998) Exact Correlation Functions of Bethe Lattice Spin Models in External Magnetic Fields. Physical Review E, 58, 1644. http://dx.doi.org/10.1103/PhysRevE.58.1644
[22] Albayrak, E. and Yigit, A. (2006) Mixed Spin-3/2 and Spin-5/2 Ising System on the Bethe Lattice. Physics Letters A, 353, 121-129. http://dx.doi.org/10.1016/j.physleta.2005.12.077

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.