Electronic phase transitions in the Falicov-Kimball model

Abstract

The finite temperature properties of the 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 specific heat coefficient (γ), as functions of temperature ( τ= k B T) and f-level energy ( E f). A number of remarkable results are found. (i) In all cases n f is a smooth function 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 wel 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.