  It is shown that the bond-decorated Ising model is a realistic model for
certain real magnetic compounds containing lanthanide ions. The lanthanide ion
plays the role of Ising spin. The required conditions on the crystal-field
spectrum of the lanthanide ion for the model to be valid are discussed and
found to be in agreement with several recent ab initio calculations on Dy(III)
centers. Similarities and differences between the spectra of the simple Ising
chain and the decorated Ising chain are discussed and illustrated, with
attention to level crossings in a magnetic field. The magnetic properties of
two actual examples (a [DyCuMoCu] chain and a Dy4Cr4 ring) are obtained by a
transfer-matrix solution of the decorated Ising model. g-factors of the metal
ions are directly imported from ab initio results, while exchange coupling
constants are fitted to experiment. Agreement with experiment is found to be
satisfactory, provided one includes a correction (from ab initio results) for
susceptibility and magnetization to account for the presence of excited Kramers
doublets on Dy(III).
