  We investigate the Gibbs properties of the fuzzy Potts model on the
d-dimensional torus with Kac interaction. We use a variational approach for
profiles inspired by that of Fernandez, den Hollander and Mart{\i}nez for their
study of the Gibbs-non-Gibbs transitions of a dynamical Kac-Ising model on the
torus. As our main result, we show that the mean-field thresholds dividing
Gibbsian from non-Gibbsian behavior are sharp in the fuzzy Kac-Potts model with
class size unequal two. On the way to this result we prove a large deviation
principle for color profiles with diluted total mass densities and use
monotocity arguments.
