Abstract
The authors study the Potts model on a diamond hierarchical lattice with random interactions. Using weak disorder expansions, they calculate analytically the position and the exponents of the random fixed point which appears when the specific heat exponent alpha p of the pure system becomes positive. At alpha p=0, they find how the logarithmic singularity is modified by the disorder. Lastly they suggest that this model should present Griffiths-like singularities.