Stability of Nagaoka phase, spin effective action and delocalized free holes

The Hubbard model in the limit of infinite $U$ is investigated within a projected slave fermion representation and following a previous work of the author and collaborators \cite{BFK}. The stability of the Nagaoka's phase with respect to a non vanishing concentration of holes ($\delta_h$) is analyzed by envisaging the existence of a spin effective action for itinerant magnetism of the Hubbard model. It is considered that,as the hole doping increases away from the half filled insulating limit, free holes are expected to be more delocalized. Depending on treatment for the hopping: a ferromagnetic or anti-ferromagnetic ordering might arise and the Nagaoka's phase might have some stability with respect to $\delta_h \neq 0$.