  Band ferromagnetism in strongly correlated electron systems is one of the
most challenging issue in today's condensed-matter physics. In this theoretical
work, we study the competition between kinetic term, Coulomb repulsion, and
on-site correlated disorder for various lattice geometries. Unconventional and
complex ferromagnetic phase diagrams are obtained: wide region of stability,
cascade of transitions, re-entrance, high sensitivity to the carrier
concentration and strongly inhomogeneous ground states for relatively weak
on-site potential. The direct and systematic comparison with Exact
Diagonalization shows that the Unrestricted Hartree-Fock method is unexpectedly
accurate for such systems, which allows large size cluster calculations. A
match of the order of 99.9% for weak and intermediate couplings is found,
slightly reduced to about 95% in the large repulsion regime. Nano-patterned
lattices appear to be particularly promising candidates that could, with the
tremendous progress in growing and self-organized techniques, be synthesized in
a near future.
