Abstract
The re-entrant phase transition of the Blume-Emery-Griffiths (BEG) model with no bilinear interaction is studied by mapping into the spin-1/2 Ising model. For the ferromagnetic interaction the first-order phase transition appears between the quadrupole phases. In the case of antiferromagnetic interaction a highly accurate boundary of the staggered quadrupole phase is presented for the square lattice. The low temperature parts of the phase boundaries for the simple cubic, body-centered cubic, square, honeycomb and triangular lattices are considered. We have concluded that the re-entrant phase transition certainly appears in the three dimensional lattices, but not in the two dimensional lattices.
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