Reconstruction of the finite size canonical ensemble from incomplete micro-canonical data

In this paper we discuss how partial knowledge of the density of states for a model can be used to give good approximations of the energy distributions in a given temperature range. From these distributions one can then obtain the statistical moments corresponding to eg the internal energy and the specific heat. These questions have gained interest apropos of several recent methods for estimating the density of states of spin models. As a worked example we finally apply these methods to the 3-state Potts model for cubic lattices of linear order up to 128. We give estimates of eg latent heat and critical temperature, as well as the microcanonical properties of interest.