General criteria for ferromagnetism in the Hubbard model

A method of wide applicability is presented for evaluating the ferromagnetic susceptibility. This leads to expressions for the ferromagnetic threshold in various approximations to the spectral weight function, and it is found that a modified Stoner criterion can always be defined. For the single-band Hubbard model the absence of an instability in the CPA is confirmed, while details are given of the magnetisation to be expected in a twofold degenerate semi-elliptic band.