Dynamical Susceptibility for Interacting Electrons in a Narrow Energy Band

An approximate expression for the dynamical susceptibility χ ( q , ω) of the paramagnetic phase of an interacting electron system in a narrow energy band is derived. The treatment is based on the “method of spectral moments”, χ ( q , ω) is used to look for instabilities of the paramagnetic state toward ferromagnetic ordering. If the number of electrons is less than the number of sites, χ ( q , ω) signals the possibility of two different types of ferromagnetism for both the s.c. and b.c.c. structure, while the paramagnetic system is stable for the f.c.c. structure. For the f.c.c.‐lattice a single ferromagnetic solution exists, if the band is more than half‐filled.