SEGREGATION IN THE FALICOV-KIMBALL MODEL

The ground state of the one-dimensional Falicov-Kimball model is considered for large values of the interaction strength U. If the ion density-rho(i) = p/q (p and q relatively prime) is rational and equals the electron density-rho(e) we prove that for U > U(c)hom (q) the ion configuration is the most homogeneous one. If 0 < rho(e) < rho(i) and U > U(c)seg (rho(e)/rho(i)) we prove that all the ions condense into one large cluster. This last result proves a recent conjecture known as the segregation principle.