RIGOROUS BOUNDS FOR THE HELMHOLTZ FREE-ENERGY OF THE FALICOV-KIMBABA MODEL

A re-examination of the model due to Falicov and Kimball is performed on the basis of a method which is developed in this paper, and which allows to calculate rigorous upper and lower bounds for the Helmholtz free energy, starting from a finite number of moments of the density-of-electron states. In the high-temperature regime very narrow bounds are obtained, which allows to check already known approximate results from mean-field theory and the coherent-potential approximation. The conditions for the existence of phase transitions within the Falicov-Kimball model are analyzed in the light of our results. The relation between the moments of the density of states of a pure matrix and those of a random binary alloy, which are required in our calculation, are derived in an Appendix. © 1979 The American Physical Society.