Saturated and non-saturated ferromagnetism in the Hubbard model with strong correlations

Abstract The stability of saturated and non-saturated ferromagnetism in the Hubbard model is considered in terms of the Green's functions for the Hubbard's many-electron operators. An analysis of earlier approximations and their shortcomings is performed. Various versions of the self-consistent approximations based on the 1 / z -expansion in the X-operator formalism are considered. It is demonstrated that the account of longitudinal fluctuations turns out to be essential for description of the non-saturated state. The corresponding pictures of density of states are obtained, “Kondo” density-of-states singularities owing to spin-flip processes being analyzed.