Nagaoka ferromagnetism in the two-dimensional infinite-U Hubbard model

We present different numerical calculations based on variational quantum Monte Carlo simulations supporting a ferromagnetic ground-state for finite and small hole densities in the two-dimensional infinite-$U$ Hubbard model. Moreover, by studying the energies of different total spin sectors, these calculations strongly suggest that the paramagnetic phase is unstable against a phase with a partial polarization for large hole densities $\delta \sim 0.40$ with evidence for a second-order transition to the paramagnetic large doping phase.