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 cubiclattice using the heating algorithm improved from the Creutz cellularautomaton (CCA) under periodic boundary conditions. The universality ofthe model are obtained for re-entrant and double re-entrant phasetransitions which occur at certain D/J and K/J parameters,with J and K representing the nearest-neighbour bilinear andbiquadratic interactions, and D being the single-ion anisotropy parameter.The values of static critical exponents β, γ and νare estimated within the framework of the finite-size scaling theory.The results are compatible with the universal Ising critical behaviourfor all continuous phase transitions in these ranges.
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