  In this note we study the block spin mean-field Potts model, in which the
spins are divided into $s$ blocks and can take $q\ge 2$ different values
(colors). Each block is allowed to contain a different proportion of vertices
and behaves itself like a mean-field Ising/Potts model which also interacts
with other blocks according to different temperatures. Of particular interest
is the behavior of the magnetization, which counts the number of colors
appearing in the distinct blocks. We prove central limit theorems for the
magnetization in the generalized high temperature regime and provide a moderate
deviation principle for its fluctuations on lower scalings. More precisely, the
magnetization concentrates around the uniform vector of all colors with an
explicit, but singular, Gaussian distribution. In order to remove the singular
component, we will also consider a rotated magnetization, which enables us to
compare our results to various related models.
