Abstract
The spin-1 Ising model with bilinear (J) and biquadratic (K) nearest-neighbor exchange interactions and a single-ion potential (\ensuremath{\Delta}), 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.
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