Rényi Entropy of Zeta-Urns

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 Rényi 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 Rényi entropy and its singularities, which depend on both the value of the power law in the zeta-urn and the order of the Rényi entropy under consideration