The two-dimensional Falicov-Kimball model at finite temperatures: numerical studies

The finite temperature properties of the spinless Falicov-Kimball model are studied in two dimensions using small-cluster exact-diagonalization calculations. The resultant exact solutions are used to examine the f-state occupation (n _f), the specific heat (C) and the density of doubly occupied sites (d) as functions of temperature (τ), f-level energy (E _f) and the interaction strength U. A number of remarkable results are found. (i) In all cases nf and d are smooth functions of τ and E _f. No discontinuous transitions occur at finite temperatures. (ii) The specific-heat curves exhibit a broad single-peak structure of Shottky form (‖E _f‖ large), as well as a two-peak structure consisting of a sharp peak of Ising type followed by a broad peak of Shottky type (‖E _f‖ small). (iii) The specific-heat coefficient is extremely enhanced at low temperatures for some values of E _f. (iv) Depending on a range of parameters used, the system exhibits intermediate-valence behavior as well as some features of heavy-fermion behavior. The results are independent of the size of clusters for a wide range of parameters and can be used to interpret much of the experimental data of rare-earth compounds. Finally, the f-electron density-density correlation functions are calculated and the U-dependence of the critical temperature is discussed.