Solvable cases of the general spin-one Ising model on the honeycomb lattice

We consider a general spin-1 Ising model on the honeycomb lattice and propose a systematic method for obtaining its solvable cases. The method is based on a sequence of transformations which produces a path between the spin-1 and spin-½ Ising models. Considering necessary conditions for performing the transformations and the solvability of the resulting spin-½ system, we recover the known and find some new nontrivial ‘exactly solvable’ subspaces in the parameter space of the spin-1 Ising model.