Ground states of the spinless Falicov-Kimball model

We present some exact results for the ground states of the Falicov-Kimball model outside the symmetry point. Three ion configurations have been considered: the chessboard configuration and the completely empty and the fully occupied configurations. Using a method based on Tchebycheff-Markov inequalities, we determine domains in the plane of chemical potentials ${\mu }_e$ and ${\mu }_i$, where these configurations are ground states.