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Abstract
We discuss the relevance of the improved mean-field slave-fermion theory to describe
the Nagaoka (\(U=\infty\)) limit of the Hubbard model. In this theory the crucial on-site
constraint of no double electron occupancy is taken into account rigorously prior
to the mean-field approximation. At one-loop approximation the effective mean-field
action shows a long-range ferromagnetic order over the whole doping range. This indicates
that the slave-fermion mean-field theory does not constitute an appropriate framework
to describe the physics of the Nagaoka phase. We discuss the drawbacks of this mean-field
theory and present some results on the derivation of a low-energy effective spin action
to describe the Nagaoka phase beyond the mean-field approximation.