  The random quantum $q$-state clock and Potts models are studied in 2 and 3
dimensions. The existence of Griffiths phases is tested in the 2D case with
$q=6$ by sampling the integrated probability distribution of local
susceptibilities of the equivalent McCoy-Wu 3D classical modelswith Monte Carlo
simulations. No Griffiths phase is found for the clock model. In contrast,
numerical evidences of the existence of Griffiths phases in the random Potts
model are given and the Finite Size effects are analyzed. The critical point of
the random quantum clock model is then studied by Strong-Disorder
Renormalization Group. Despite a chaotic behavior of the Renormalization-Group
flow at weak disorder, evidences are given that this critical behavior is
governed by the same Infinite-Disorder Fixed Point as the Potts model,
independently from the number of states $q$.
