Falicov-Kimball model

Freericks, J. K. Zlatic, V. 2003 Exact dynamical mean field theory of the Falicov-Kimball model, Rev. Mod. Phys. 75, 1333-1382. (doi 10.1103/RevModPhys.75.l333)... 

The phase transition is theoretically treated, for example, by Mahanti et al. [9] with the essentially localized model ( Rare Earth Elements C7,1983, p. 311) or by Alascio, L6pez [10], Kocharyan, Khomskii [11], Kanda et al. [12] with the Falicov-Kimball model (see Rare Earth Elements C7, 1983, p. 306). 

The extended Falicov-Kimball model with hybridization ( Rare Earth Elements C 7, 1983, p. 306) is used by Kanda etal. [26] to calculate the electron occupation number of the conduction band as a function of the localized level. The Falicov-Kimball model is also used to describe the intermediate valence state and the phase transition by Schweitzer [27], Singh et al. [28]. 

The pressure-induced semiconductor-metal transitions of SmSei xSx solid solutions are discontinuous for x>0.2 and continuous forx<0.2 as detected by electrical resistivity q versus pressure measurements. The strength of the first-order phase transition (expressed by Ag/g p where Ag is the resistivity jump and Qtr s the resistivity at the transition pressure Ptr) decreases smoothly to zero at x = 0.2. This composition is characterized by a sharp break in slope at 34.6 kbar when q versus p is plotted but no hysteresis is noticed as pressure is released. Transition pressure p r and Ag/ptr in comparison with the theoretical phase transition strength (calculated with a modified Falicov-Kimball model) as a function of composition are shown in Fig. 81, p. 170, Bucher, Maines [2], also see Bucher et al. [3]. The change from continuous to discontinuous transition is interpolated to be at x = 0.28 the experimental value is 0.25 (determination technique not given in the paper), Narayan, Ramaseshan [4]. The course of the configuration crossover f d°- f d for Sm(Se,S) under pressure is illustrated by Wilson [5]. 

Thus SmS with its first-order transition was, historically seen, not the best example to study the valence transition in the Sm chalcogenides, but with its low transition pressure and simple alloying it functioned as a pathfinder substance for the others. Only gradually, with more subtle high-pressure techniques, the new picture penetrates the surface. However, there is the old and well known Falicov-Kimball (1969) model which predicted the valence transition in the Sm chalcogenides as due to electronic effects, which seems now to find a late confirmation. 

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