Ferromagnetism in the Hubbard model: Influence of the lattice structure

By use of the spectral density approach the influence of the lattice structure on the possibility of ferromagnetism in the single band Hubbard model is investigated. The d=\infty hypercubic lattice does not show magnetic phase transitions of second order irrespective of the strength of the Coulomb coupling. However, first order transitions to finite magnetic moments, not visible as singularities of the paramagnetic susceptibility, may appear in the very strong coupling regime. In d=3 second order transitions are found but only for very strong couplings, where the non-locality of the electronic self-energy acts in favour of the spontaneous magnetic moment. The influence of the non-local part of the self-energy is particularly strong for lattices with small coordination number. The non-bipartite fcc lattice exhibits saturated ferromagnetism for all band occupations $1\le n\le 2$ while for less than half filled bands ($0\le n\le 1$) the system remains in any case paramagnetic, and that for d=3 as well as d=\infty. The Curie temperature runs through a maximum at about $n=1.4$ and vanishes for $n\to 1$ and $n\to 2$.