Abstract
The q-state Potts model on the triangular lattice with nearest-neighbour interactions and three-site interactions in half of the triangular faces is considered. The exact duality relation is re-examined from the point of view of determining its critical point. Using the continuity and uniqueness arguments the authors determine the exact critical point in the ferromagnetic model. It is argued that a transition exists in an antiferromagnetic model only for q=3. A conjecture is then made on the phase diagram for the q=3 isotropic model. These results are used to determine the exact criticality of a dilute Potts model on the honeycomb lattice.
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