Ground state properties of the falicov-kimball model in the strong coupling limit

We present some analytic results concerning the ground state of the one-dimensional Falicov-Kimball model in the strong coupling limit. Using the perturbation theory, we find: (i) The well-expected phase segregation takes place for ¦U¦ (U is the interaction strength), (ii) For finiteU there exists the critical value of the interaction strengthU =U_c, below which the segregated phase — an incoherent mixture of the empty and full lattices cannot be the ground state of the model. We give the analytical expression for this boundary. Finally, we discuss the phase diagram of the model for some special configuration of ions.