The microscopic basis for the stability of itinerant ferromagnetism in
correlated electron systems is examined. To this end several routes to
ferromagnetism are explored, using both rigorous methods valid in arbitrary
spatial dimensions, as well as Quantum Monte Carlo investigations in the limit
of infinite dimensions (dynamical mean-field theory). In particular we discuss
the qualitative and quantitative importance of (i) the direct Heisenberg
exchange coupling, (ii) band degeneracy plus Hund's rule coupling, and (iii) a
high spectral density near the band edges caused by an appropriate lattice
structure and/or kinetic energy of the electrons. We furnish evidence of the
stability of itinerant ferromagnetism in the pure Hubbard model for appropriate
lattices at electronic densities not too close to half-filling and large enough
U. Already a weak direct exchange interaction, as well as band degeneracy, is
found to reduce the critical value of U above which ferromagnetism becomes
stable considerably. Using similar numerical techniques the Hubbard model with
an easy axis is studied to explain metamagnetism in strongly anisotropic
antiferromagnets from a unifying microscopic point of view.Comment: 11 pages, Latex, and 6 postscript figures; Z. Phys. B, in pres