The spin-1 Ising model with bilinear (J) and biquadratic (K) nearest-neighbor exchange interactions and a single-ion potential (Δ), a model introduced by Blume, Emery, and Griffiths (BEG), is studied on a honeycomb lattice. The exact solution of the BEG model is obtained for a certain relation K=K(J). Also an approximate treatment of the BEG model outside the surface, in the space of coupling constants, given by the relation above is discussed. Finally a digression is made on the critical temperature of the spin-1 Ising model.

• Received 24 May 1989

DOI:https://doi.org/10.1103/PhysRevLett.63.660