  We compare different approximation schemes for investigating ferromagnetism
in the periodic Anderson model. The use of several approximations allows for a
detailed analysis of the implications of the respective methods, and also of
the mechanisms driving the ferromagnetic transition. For the Kondo limit, our
results confirm a previously proposed mechanism leading to ferromagnetic order,
namely an RKKY exchange mediated via the formation of Kondo screening clouds in
the conduction band. The contrary case is found in the intermediate-valence
regime. Here, the bandshift correction ensuring a correct high-energy expansion
of the self-energy is essential. Inclusion of damping effects reduces stability
of the ferromagnetic phase.
