Phase separation in the strongly correlated Falicov-Kimball model in infinite dimensions

Phase separation in the strongly correlated Falicov-Kimball model in infini te dimensions is examined. We show that the phase separation can occur for any values of the interaction constant J* when the site energy epsilon(0) o f the localized electrons is equal to zero. Electron-poor regions always ha ve homogeneous state and electron-rich regions have chessboard state for J* greater than or equal to 0.03, chessboard state or homogeneous state in de pendence upon temperature for 0 < J* < 0.03 and homogeneous state for J* = 0. For J* = 0 and T = 0, phase separation (segregation) occurs at -1 < epsi lon(0) < 0. The obtained results are exact for the Bethe lattice with infin ite number of the nearest neighbours.