  The ferromagnetism of Au nanograins is analysed based on a two-dimensional
itinerant lattice model with on-site Coulomb repulsion, many-body spin-orbit
interactions, and holding two hybridized bands, one correlated and one
uncorrelated. Using periodic boundary conditions in both directions, an exact
ferromagnetic ground state is deduced for this non-integrable system by
applying special techniques based on positive semidefinite operators.
