Ground-state properties of the antiferromagnetic potts model in an external field

The ground-state properties of the antiferromagnetic q-state Potts model in an external field are studied. At the upper critical field this model may be mapped onto a hard-core lattice gas with activity z = q ?1. This allows us to get some exact results for the triangular lattice on which the corresponding hard hexagon problem has been recently solved by Baxter.