Phase transitions in the three-dimensional Falicov–Kimball model

The classical Monte-Carlo method is used to study the finite-temperature properties of the three-dimensional ( D = 3 ) Falicov–Kimball model in the symmetric case. It is shown that the critical temperature of the phase transition from the low-temperature ordered phase to the high-temperature disordered phase in D = 3 is considerably enhanced in comparison to the two-dimensional case ( D = 2 ). A significant shift to higher values of the Coulomb interaction U (with respect to D = 2 ) is also found for the critical point U c , at which the nature of the phase transition changes from the first to second order. In addition, the temperature dependence of the itinerant electron density of states (DOS) is analysed. For very low-temperatures we have observed a formation of a fine structure inside the principal gap that transforms to a pseudo-gap at higher temperatures and becomes temperature independent for sufficiently large temperatures. In this temperature region we have calculated DOS for different Coulomb interactions and found the Mott-Hubbard transition.