Breakdown of the Nagaoka phase at finite doping
  The Nagaoka ($U=\infty$) limit of the Hubbard model on a square lattice is mapped onto the itinerant-localized Kondo model at infinitely strong coupling. Such a model is well suited to perform quantum Monte Carlo (QMC) simulations to compute spin correlation functions. This model is shown to exhibit no short-range ferromagnetic (FM) spin correlations at any doping $\delta\ge 0.01$ and finite temperature, $T=0.1t$. Our simulations give no indication that there is a tendency towards ferromagnetic ordering in the ground state. 
Ilya Ivantsov, Alvaro Ferraz and Evgenii Kochetov
cond-mat.str-el