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

Phase separation in the strongly correlated Falicov-Kimball model in infinite dimensions is examined. We show that the phase separation can occur for any values of the interaction constant J^* when the site energy of the localized electrons is equal to zero. Electron-poor regions always have homogeneous state and electron-rich regions have chessboard state for , chessboard state or homogeneous state in dependence upon temperature for 0<J ^* <0.03 and homogeneous state for J ^* =0. For J ^* =0 and T=0, phase separation (segregation) occurs at .The obtained results are exact for the Bethe lattice with infinite number of the nearest neighbours. Received 1 December 1998 and Received in final form 12 April 1999