Phase diagrams of extended Hubbard models in the atomic limit

We consider phase diagrams of a family of two-dimensional Hubbard-like models in the atomic limit. We start with the ground state phase diagram of the Hubbard model augmented by a nearest-neighbour repulsion and study the effect of a perturbation by temperature. This enables us to reveal the origin of the tricritical behaviour found earlier in a mean field approximation. Then we study perturbations by next nearest-neighbour repulsive interactions, Ising-like nearest- and next nearest-neighbour magnetic interactions and by temperature. Finally the ground state phase diagram corresponding to a class of long range repulsive and Ising-like interactions is considered. While such repulsive interactions generate infinitely many charge-ordered phases, we argue that an arbitrary small narrow band may prevail and leave only finitely many of them.