Density-of-states picture and stability of ferromagnetism in the highly correlated Hubbard model

The problem of stability of saturated and nonsaturated ferromagnetism in the Hubbard model is considered in terms of the one-particle Green's functions. Approximations by Edwards and Hertz and some versions of the self-consistent approximations based on the 1/z expansion are considered. The account of longitudinal fluctuations turns out to be essential for description of the nonsaturated state. The corresponding pictures of density of states are obtained. Kondo density-of-states singularities owing to spin-flip processes are analyzed. The critical electron concentrations for instabilities of saturated ferromagnetism and paramagnetic state are calculated for various lattices. Drawbacks of various approximations are discussed. A comparison with the results of previous works is performed.