Rnyi entropy of zeta urns

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