  The problem of ferromagnetism -- associated with a ground state with maximal
total spin -- is discussed in the framework of a hard-core model, which forbids
the occupancy at each site with more than one particle. It is shown that the
emergence of ferromagnetism on finite square lattices crucially depends on the
statistics of the particles. Fermions (electrons) lead to the well-known
instabilities for finite hole densities, whereas for bosons (with spin)
ferromagnetism appears to be stable for all hole densities.
