A systematic investigation of the microscopic conditions stabilizing itiner
ant ferromagnetism of correlated electrons in a single-band model is presen
ted. Quantitative results are obtained by quantum Monte Carlo simulations f
or a model with Hubbard interaction U and direct Heisenberg exchange intera
ction F within the dynamical mean-field theory. Special emphasis is placed
on the investigation of (i) the distribution of spectral weight in the dens
ity of states, (ii) the importance of,genuine correlations, and (iii) the s
ignificance of-the direct exchange, for the stability of itinerant ferromag
netism at finite temperatures. We find that already a moderately strong pea
k in the density of states near the band edge suffices to stabilize ferroma
gnetism at intermediate U values in a broad range of electron densities n.
Correlation effects prove to be essential: Slater-Hartree-Fock results for
the transition temperature are both qualitatively and quantitatively incorr
ect. The nearest neighbor Heisenberg exchange does not, in general, play a
decisive role. Detailed results for the magnetic phase diagram as a functio
n of U, F, n, temperature T, and the asymmetry of the density of states are
presented and discussed. [SO163-1829(98)08943-7].