Lattice dependence of saturated ferromagnetism in the Hubbard model

We investigate the instability of the saturated ferromagnetic ground state (Nagaoka state) in the Hubbard model on various lattices in dimensions $d=2\mathrm{}$ and $d=3\mathrm{}$. A variational resolvent approach is developed for the Nagaoka instability both for $U=\infty$ and for $U<\mathrm{}\infty$ which can easily be evaluated in the thermodynamic limit on all common lattices. Our results significantly improve former variational bounds for a possible Nagaoka regime in the ground-state phase diagram of the Hubbard model. We show that a pronounced particle-hole asymmetry in the density of states and a diverging density of states at the lower band edge are the most important features in order to stabilize Nagaoka ferromagnetism, particularly in the low-density limit.