The two-state spinless Falicov-Kimball model on a one-dimensional latt
ice is studied by means of well-controlled numerical procedures. Restr
icted phase diagrams in the grand-canonical ensemble and at zero tempe
rature are constructed. The evolution of these phase diagrams, as the
interaction parameter U is varied, along with the band structures corr
esponding to configurations of localized particles (ions) and densitie
s of mobile particles (electrons), is monitored. The changes observed
enable us to draw conclusions for the complete phase diagram and to ma
ke a qualitative plot of such a diagram.