  We construct a variational wave function to study whether a fully polarized
Fermi sea is energetically stable against a single spin flip. Our variational
wave function contains sufficient short-range correlation at least to the same
level as Gutzwiller's projected wave function. For Hubbard lattice model and
continuum model with pure repulsive interaction, we show a fully polarized
Fermi sea is generally unstable even when the repulsive strength becomes
infinite. While for a resonance model, ferromagnetic state is possible if the
s-wave scattering length is positive and sufficiently large, and the system is
prepared in scattering state orthogonal to molecular bound state. However, we
can not rule out the possibility that more exotic correlation can destabilize
the ferromagnetic state.
