  We calculate analytically the Renyi entropy for the zeta-urn model with a
Gibbs measure definition of the micro-state probabilities. This allows us to
obtain the singularities in the R\'enyi entropy from those of the thermodynamic
potential, which is directly related to the free energy density of the model.
We enumerate the various possible behaviours of the R\'enyi entropy and its
singularities, which depend on both the value of the power law in the zeta-urn
and the order of the R\'enyi entropy under consideration
