The spinless Falicov-Kimball model away from half-filling

The one-dimensional spinless Falicov-Kimball (FKM) model is studied in the strong coupling limit away from half-filling. The small-cluster exact-diago nalization calculations are employed to obtain valence transitions in the g round state and for finite temperatures. It is found that in the ground sta te, the model describes continuous Valence transitions for small band-filli ngs and both continuous and discontinuous transitions near half-filling. At finite temperatures, only continuous valence transitions are obtained. The valence is integer at low temperatures for small band-fillings and in othe r cases, it takes only intermediate Values.