Critical Exponents for the Re-entrant Phase Transitions in the Three-Dimensional Blume--Emery--Griffiths Model on the Cellular Automaton
N. Seferoglu1, B. Kutlu2
1GaziUniversitesi, Fen Bilimleri Enstitusu, Fizik Anabilim Dal\i, Ankara, Turkey 2GaziUniversitesi, Fen-Edebiyat Fakultesi, Fizik Bolumu, 06500 Teknikokullar, Ankara, Turkey
Critical Exponents for the Re-entrant Phase Transitions in the Three-Dimensional Blume--Emery--Griffiths Model on the Cellular Automaton
N. Seferoglu1;B. Kutlu2
1GaziUniversitesi, Fen Bilimleri Enstitusu, Fizik Anabilim Dal\i, Ankara, Turkey 2GaziUniversitesi, Fen-Edebiyat Fakultesi, Fizik Bolumu, 06500 Teknikokullar, Ankara, Turkey
摘要The critical behaviour of the three-dimensional Blume--Emery--Griffiths (BEG) model is investigated at D/J=0, -0.25 and -1 in the range of -1≤K/J≤0 for J=100. The simulations are carried out on a simple cubic lattice using the heating algorithm improved from the Creutz cellular automaton (CCA) under periodic boundary conditions. The universality of the model are obtained for re-entrant and double re-entrant phase transitions which occur at certain D/J and K/J parameters, with J and K representing the nearest-neighbour bilinear and biquadratic interactions, and D being the single-ion anisotropy parameter. The values of static critical exponents β, γ and υ are estimated within the framework of the finite-size scaling theory. The results are compatible with the universal Ising critical behaviour for all continuous phase transitions in these ranges.
Abstract：The critical behaviour of the three-dimensional Blume--Emery--Griffiths (BEG) model is investigated at D/J=0, -0.25 and -1 in the range of -1≤K/J≤0 for J=100. The simulations are carried out on a simple cubic lattice using the heating algorithm improved from the Creutz cellular automaton (CCA) under periodic boundary conditions. The universality of the model are obtained for re-entrant and double re-entrant phase transitions which occur at certain D/J and K/J parameters, with J and K representing the nearest-neighbour bilinear and biquadratic interactions, and D being the single-ion anisotropy parameter. The values of static critical exponents β, γ and υ are estimated within the framework of the finite-size scaling theory. The results are compatible with the universal Ising critical behaviour for all continuous phase transitions in these ranges.
N. Seferoglu;B. Kutlu. Critical Exponents for the Re-entrant Phase Transitions in the Three-Dimensional Blume--Emery--Griffiths Model on the Cellular Automaton[J]. 中国物理快报, 2007, 24(7): 2040-2043.
N. Seferoglu, B. Kutlu. Critical Exponents for the Re-entrant Phase Transitions in the Three-Dimensional Blume--Emery--Griffiths Model on the Cellular Automaton. Chin. Phys. Lett., 2007, 24(7): 2040-2043.
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2007, Vol. 24 
