  The two-dimensional interacting electron gas at Landau level filling factor
$\nu =1$ and temperature $T=0$ is a strong ferromagnet; all spins are
completely aligned by arbitrarily weak Zeeman coupling. We report on a
theoretical study of its thermodynamic properties using a many-body
perturbation theory approach and concentrating on the recently measured
temperature dependence of the spin magnetization. We discuss the interplay of
collective and single-particle aspects of the physics and the opportunities for
progress in our understanding of itinerant electron ferromagnetism presented by
quantum Hall ferromagnets.
