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In this work, a lower bound for the ground state energy of theFalicov-Kimball model for intermediate densities is derived. The explicitderivation is important in the proof of the conjecture of segregation of thetwo kinds of fermions in the Falicov-Kimball model, for sufficiently largeinteractions. This bound is given by a bulk term, plus a term proportional tothe boundary of the region devoid of classical particles. A detailed proof ispresented for density n=1/2, where the coefficient 10^(-13) is obtained for theboundary term, in two dimensions. With suitable modifications the method canalso be used to obtain a coefficient for all densities.Comment: 8 pages, 2 figure

Lower bound for the segregation energy in the Falicov Kimball model