Re-entrant phase transitions of the Blume-Emery-Griffiths model: II. Staggered quadrupole phase boundaries forJ 1=0 in the two and three dimensions

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