  We complete the investigation of the Gibbs properties of the fuzzy Potts
model on the d-dimensional torus with Kac interaction which was started by
Jahnel and one of the authors. As our main result of the present paper, we
extend the previous sharpness result of mean-field bounds to cover all possible
cases of fuzzy transformations, allowing also for the occurrence of Ising
classes. The closing of this previously left open Ising-gap involves an
analytical argument showing uniqueness of minimizing profiles for certain
non-homogeneous conditional variational problems.
