Critical exponents for the re-entrant phase transitions in the three-dimensional Blume-Emery-Griffiths model on the cellular automaton

Seferoglu N. , Kutlu B.

CHINESE PHYSICS LETTERS, cilt.24, sa.7, ss.2040-2043, 2007 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 24 Konu: 7
  • Basım Tarihi: 2007
  • Doi Numarası: 10.1088/0256-307x/24/7/070
  • Sayfa Sayıları: ss.2040-2043


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 beta, gamma and nu 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.