  The magnetic ground-state properties of the periodic Anderson model with a
regular depletion of the correlated sites are analyzed within different
theoretical approaches. We consider the model on the one-dimensional chain and
on the two-dimensional square lattice with hopping between nearest neighbors.
At half-filling and with correlated impurities present at every second site,
the depleted Anderson lattice is the most simple system where the indirect
magnetic coupling mediated by the conduction electrons is ferromagnetic. We
discuss the underlying electronic structure and the possible mechanisms that
result in ferromagnetic long-range order. To this end, different numerical and
analytical concepts are applied to the depleted Anderson and also to the
related depleted Kondo lattice and are contrasted with each other. This
includes numerical approaches, i.e. Hartree-Fock theory, density-matrix
renormalization and dynamical mean-field theory, as well as analytical
concepts, namely a variant of the Lieb-Mattis theorem and the concept of
flat-band ferromagnetism, and finally perturbative approaches, i.e. the
effective RKKY exchange in the limit of weak and the "inverse indirect magnetic
exchange" in the limit of strong coupling between the conduction band and the
impurities.
