  The two-dimensional Falicov-Kimball (FK) model is analyzed using Monte Carlo
method. In the case of concentrations of both itinerant and localized particles
equal to 0.5 we determine temperature dependence of specific heat, charge
density wave susceptibility and density-density correlation function. In the
weak interaction regime we find a first order transition to the ordered state
and anomalous temperature dependence of the correlation function. We construct
the phase diagram of half-filled FK model. Also, the role of
next-nearest-neighbor hopping on the phase diagram is analyzed. Lastly, we
discuss the density of states and the spectral functions for the mobile
particles in weak and strong interaction regime.
