On the theory of the Mott transition in the paramagnetic phase

A critical consideration of some approaches to the metal-insulator transition problem, starting from the many-electron representation, is carried out within the framework of the Hubbard and classical s-d models in the far-paramagnetic region. The analytical properties of the corresponding one-electron Green functions are discussed, the importance of terms of sufficiently high orders in l/z being demonstrated. The total energy, electronic specific heat and corrections to the local moment are calculated. The Hubbard-III approximation in the Hubbard model (but not in the s-d model) is shown to lead to difficulties when calculating thermodynamic properties.