Strong coupling phases of the t-t' Hubbard model

We study the strong coupling regime of the $t-t'$ Hubbard model,filled up to the level of the van Hove singularities, by means of an exact diagonalization approach. We characterize the different phases of the model by the different sectors of the Hilbert space with given quantum numbers. By looking for the ground state of the system, we find essentially the competition between a state with incipient ferromagnetism and other mimicking a $d$-wave condensate, which has the lowest energy in a large region of the phase space.