The ferrimagnetic phase of the Blume-Emery-Griffiths model on the cellular automaton

• Authors: Nurgül Seferoğlu , Bülent Kutlu
• Languages of publication: EN

Abstracts

EN

The Blume-Emery-Griffiths model is simulated using the cooling algorithm which is improved from the Creutz cellular automaton (CCA) under periodic boundary conditions. The simulations are carried out on a simple cubic lattice at K/J = −1.5 in the range of −3.5 < D/J < 0.5, with J and K representing the nearestneighbour bilinear and biquadratic interactions, D being the single-ion anisotropy parameter. The phase diagram characterizing phase transition of the model is obtained. We found different kinds of phase transitions between the ferromagnetic, quadrupolar, staggered quadrupolar and ferrimagnetic phases for K/J = −1.5. In particular, the region of the phase diagram containing a ferrimagnetic phase is explored and compared to those obtained by other methods. The simulations confirm that the ferrimagnetic phase occurs in the narrow interval −3.006 ≤ D/J < −3. This result is in a good agreement with Monte Carlo renormalization group and closer to the cluster variation method result than the mean field approximation result.

Keywords

EN

Blume Emery Griffiths model; ferrimagnetic phase; Creutz cellular automaton; simple cubic lattice

Discipline

• 64.60.De: Statistical mechanics of model systems (Ising model, Potts model, field-theory models, Monte Carlo techniques, etc.)
• 64.60.an: Finite-size systems
• 75.10.Hk: Classical spin models
• 75.50.Gg: Ferrimagnetics

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2008
• Volume: 6
• Issue: 2
• Pages: 230-237

Dates

published

1 - 6 - 2008

online

26 - 3 - 2008

Contributors

author

Nurgül Seferoğlu

• Fen Bilimleri Enstitüsü, Fizik Anabilim Dali, Gazi Üniversitesi, Ankara, Turkey

author

Bülent Kutlu

• Fen-Edebiyat Fakültesi, Fizik Bölümü, Gazi Üniversitesi, 06500, Teknikokullar, Ankara, Turkey

References

• [1] F. Rys, Helv. Phys. Acta 42, 608 (1969)
• [2] M. Blume, V.J. Emery, R.B. Griffiths, Phys. Rev. A 4, 1071 (1971) http://dx.doi.org/10.1103/PhysRevA.4.1071[Crossref]
• [3] J. Lajzerowicz, J. Sivardiere, Phys. Rev. A 11, 2079 (1975) http://dx.doi.org/10.1103/PhysRevA.11.2079[Crossref]
• [4] J. Sivardiere, J. Lajzerowicz, Phys. Rev. A 11, 2090 (1975) http://dx.doi.org/10.1103/PhysRevA.11.2090[Crossref]
• [5] H.H. Chen, P.M. Levy, Phys. Rev. B 7, 4267 (1973) http://dx.doi.org/10.1103/PhysRevB.7.4267[Crossref]
• [6] W. Hoston, A.N. Berker, Phys. Rev. Lett. 67, 1027 (1991) http://dx.doi.org/10.1103/PhysRevLett.67.1027[Crossref]
• [7] R.R. Netz, A.N. Berker, Phys. Rev. B 47, 15019 (1993)
• [8] W. Hoston, A.N. Berker, J. Appl. Phys. 70, 6101 (1991) http://dx.doi.org/10.1063/1.350059[Crossref]
• [9] S. Lapinkas, A. Rosengren, Phys. Rev. B 49, 15190 (1994)
• [10] C. Ekiz, M. Keskin, Phys. Rev. B 66, 054105 (2002)
• [11] J.W. Tucker, T. Balcerzak, M. Gzik, A. Sukiennicks, J. Magn. Magn. Mater. 187, 381 (1998) http://dx.doi.org/10.1016/S0304-8853(98)00136-X[Crossref]
• [12] M. Keskin, A. Erdinç, J. Magn. Magn. Mater. 283, 392 (2004) http://dx.doi.org/10.1016/j.jmmm.2004.06.012[Crossref]
• [13] T. Balcerzak, M. Gzik-Szumiata, Phys. Rev. B 6013, 9450 (1999) http://dx.doi.org/10.1103/PhysRevB.60.9450[Crossref]
• [14] T. Kaneyoshi, J. Phys. Soc. Jpn. 56, 4199 (1987) http://dx.doi.org/10.1143/JPSJ.56.4199[Crossref]
• [15] I.P. Fittipalde, T. Kaneyoshi, J. Phys.-Condens. Matter 1, 6513 (1989) http://dx.doi.org/10.1088/0953-8984/1/37/001[Crossref]
• [16] R.R. Netz, Europhys. Lett. 17, 373 (1992) http://dx.doi.org/10.1209/0295-5075/17/4/016[Crossref]
• [17] Y.L. Wang, C. Wentworth, J. Appl. Phys. 61, 4411 (1987) http://dx.doi.org/10.1063/1.338392[Crossref]
• [18] Y.L. Wang, F. Lee, J. D. Kimel, Phys. Rev. B 36, 8945 (1987) http://dx.doi.org/10.1103/PhysRevB.36.8945[Crossref]
• [19] K. Kasono, I. Ono, Z. Phys. B Cond. Mat. 88, 205 (1992) http://dx.doi.org/10.1007/BF01323573[Crossref]
• [20] G.M. Zhang, C.Z. Yang, Phys. Rev. B 51, 3605 (1995) http://dx.doi.org/10.1103/PhysRevB.51.3605[Crossref]
• [21] N. Seferoğlu, B. Kutlu, Physica A 374, 165 (2007) http://dx.doi.org/10.1016/j.physa.2006.07.010[Crossref]
• [22] N. Seferoğlu, B. Kutlu, Chin. Phys. Lett. 24, 2040 (2007) http://dx.doi.org/10.1088/0256-307X/24/7/070[Crossref]
• [23] N. Seferoğlu, B. Kutlu, J. Stat. Phys. 129, 453 (2007) http://dx.doi.org/10.1007/s10955-007-9392-z[Crossref]
• [24] M. Creutz, Phys. Rev. Lett. 50, 1411 (1983) http://dx.doi.org/10.1103/PhysRevLett.50.1411[Crossref]
• [25] B. Kutlu, Int. J. Mod. Phys. C 12, 140 (2001) http://dx.doi.org/10.1142/S0129183101002747[Crossref]
• [26] B. Kutlu, A. Özkan, N. Seferoğlu, A. Solak, B. Binal, Int. J. Mod. Phys. C 16, 1933 (2005) http://dx.doi.org/10.1142/S0129183105007601[Crossref]
• [27] A. Özkan, N. Seferoğlu, B. Kutlu, Physica A 362, 327 (2006) http://dx.doi.org/10.1016/j.physa.2005.08.065[Crossref]
• [28] N. Seferoğlu, A. Özkan, B. Kutlu, Chin. Phys. Lett. 23, 2526 (2006) http://dx.doi.org/10.1088/0256-307X/23/9/049[Crossref]
• [29] N. Aktekin, In: D. Stauffer (Ed.), Annual Reviews of Computational Physics VII (World Scientific, Singapore, 2000) 1
• [30] B. Kutlu, Int. J. Mod. Phys. C 14, 1305 (2003) http://dx.doi.org/10.1142/S0129183103005443[Crossref]
• [31] B. Kutlu, Physica A 234, 807 (1997) http://dx.doi.org/10.1016/S0378-4371(96)00309-3[Crossref]
• [32] B. Kutlu, M. Kasap, S. Turan, Int. J. Mod. Phys. C 11, 561 (2000)

Identifiers

DOI

10.2478/s11534-008-0034-0