Reentrant Phase Transitions of the Blume-Emery-Griffiths Model for a Simple Cubic Lattice on the Cellular Automaton

The spin-1 Ising (BEG) model with the nearest-neighbour bilinear and biquadratic interactions and single-ion anisotropy is simulated on a cellular automaton which improved from the Creutz cellular automaton(CCA) for a simple cubic lattice. The simulations have been made for several sets of parameters $K\mathrm{/}J$ and $D\mathrm{/}J$ in the $-3<D\mathrm{/}J\le 0$ and $-1\le K\mathrm{/}J\le 0$ parameter regions. The re-entrant and double re-entrant phase transitions of the BEG model are determined from the temperature variations of the thermodynamic quantities ($M$, $Q$ and $\chi$). The phase diagrams characterizing phase transitions are compared with those obtained from other methods.