LATTICE DEPENDENCE OF SATURATED FERROMAGNETISM IN THE HUBBARD-MODEL

We investigate the instability of the saturated ferromagnetic ground s tate (Nagaoka state) in the Hubbard model on various lattices in dimen sions d=2 and d=3. A variational resolvent approach is developed for t he Nagaoka instability both for U=infinity and for U<infinity which ca n easily be evaluated in the thermodynamic limit on all common lattice s. Our results significantly improve former variational bounds for a p ossible Nagaoka regime in the ground-state phase diagram of the Hubbar d model. We show that a pronounced particle-hole asymmetry in the dens ity of states and a diverging density of states at the lower band edge are the most important features in order to stabilize Nagaoka ferroma gnetism, particularly in the low-density limit.