Coherent-Potential-Approximation Calculation on the Falicov-Kimball Model of the Metal-Insulator Transition

We solve the Falicov-Kimball model of the metal-insulator transition in the coherent-potential approximation. This yields exact results in certain limits in which molecular field theory is incorrect, and it is a better approximation over the whole range of the parameters. We find that, at least below the point at which bound states appear, all phase transitions vanish.