Abstract
The extended Falicov-Kimball model containing the next to next-nearest-neighbor hopping interaction (NNNN) is investigated using the exact diagonalization calculations in two dimensions. The f-electron density nf with the energy of f-level Ef is investigated using the allowable exact solutions. The temperature dependency of thermodynamical parameters such as specific heat(C) and entropy (S) are also studied here. The significant observations are (i) a discontinuous valence transition (insulator-to-metal) at a certain energy of f-level (Ec ) which varies with the value of NNNN interaction term (t 3), (ii) disorderedness of the system with the increasing value of t 3, (iii) the structures of single and double peaks in the specific heat versus temperature graphs varying with t 3 and E respectively.
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