  We introduce and analyze a generalization of the blocks spin Ising
(Curie-Weiss) models that were discussed in a number of recent articles. In
these block spin models each spin in one of $s$ blocks can take one of a finite
number of $q \ge 3$ values, hence the name block spin Potts model. The values a
spin can take are called colors. We prove a large deviation principle for the
percentage of spins of a certain color in a certain block. These values are
represented in an $s \times q$ matrix. We show that for uniform block sizes and
appropriately chosen interaction strength there is a phase transition. In some
regime the only equilibrium is the uniform distribution of all colors in all
blocks, while in other parameter regimes there is one predominant color, and
this is the same color with the same frequency for all blocks. Finally, we
establish log-Sobolev-type inequalities for the block spin Potts model.
