The Influence of Lattice Defects on the Ground-State Properties of the Falicov-Kimball Model in Two Dimensions

The influence of lattice defects (vacancies) on the ground-state properties of the spinless Falicov-Kimball model is studied by a well-controlled numerical method in two dimensions. It is shown that in the presence of vacancies (distributed randomly) the ground states of the Falicov-Kimball model are phase separated for small f-electron concentrations $n_f$ and exhibit the long-range order for $n_f$ near the half-filled band case $n_f$=1/2. In addition, the dependence of average f-orbital occupancy on the concentration of vacancies is calculated for a wide range of model parameters. The resultant behaviours are used to interpret the experimental data obtained for the mixed-valence system $Sm_{1-x}B_6$