  The present paper is based on our graduate lectures in condensed-matter
physics. We found that the mean-field solution of the Hubbard model is an
excellent tool to stimulate students' reflections towards the treatment of
realistic magnetic interactions. We show by detailed analytical and numerical
calculations how to find the mean-field solution of the model on a square
lattice. We then interpret the physical implications of the ground-state
magnetic phase diagram in terms of the electron density and the ratio between
the Coulomb repulsion and the electron-structure bandwidth.
