Ferromagnetism in the Hubbard model on the square lattice: Improved instability criterion for the Nagaoka state

The instability of the fully polarized ferromagnetic state (Nagaoka state) with respect to single spin flips is re-examined for the Hubbard model on the square lattice with a large family of variational wave functions which include correlation effects of the majority spins in the vicinity of the flipped spin. We find a critical hole density of $\delta_{cr} = 0.251$ for $U = \infty$ and a critical coupling of $U_{cr} = 77.7 t$. Both values improve previous variational results considerably.