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

TL;DR

This paper investigates the stability of ferromagnetism in the Hubbard model using Green's functions, analyzing density of states and fluctuations to understand phase stability and critical electron concentrations.

Contribution

It introduces a detailed density-of-states analysis and compares various approximation methods for ferromagnetism stability in the Hubbard model.

Findings

Longitudinal fluctuations are crucial for non-saturated states.

Density of states features Kondo singularities from spin-flip processes.

Critical electron concentrations for phase instabilities are calculated.

Abstract

The problem of stability of saturated and non-saturated 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 non-saturated 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.