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, vol.24, no.7, pp.2040-2043, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 7
  • Publication Date: 2007
  • Doi Number: 10.1088/0256-307x/24/7/070
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2040-2043
  • Gazi University Affiliated: Yes


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.