  We study a variant of the ferromagnetic Potts model, recently introduced by
Tamura, Tanaka and Kawashima, consisting of a ferromagnetic interaction among
$q$ "visible" colours along with the presence of $r$ non-interacting
"invisible" colours. We introduce a random-cluster representation for the
model, for which we prove the existence of a first-order transition for any
$q>0$, as long as $r$ is large enough. When $q>1$, the low-temperature regime
displays a $q$-fold symmetry breaking. The proof involves a Pirogov-Sinai
analysis applied to this random-cluster representation of the model.
