We propose to use the Contractor Renormalization (CORE) technique in order to
derive effective models for quantum magnets in a magnetic field. CORE is a
powerful non-perturbative technique that can reduce the complexity of a given
microscopic model by focusing on the low-energy part. We provide a detailed
analysis of frustrated spin ladders which have been widely studied in the past:
in particular, we discuss how to choose the building block and emphasize the
use of their reduced density matrix. With a good choice of basis, CORE is able
to reproduce the existence or not of magnetization plateaux in the whole phase
diagram contrary to usual perturbation theory. We also address the issue of
plateau formation in two-dimensional bilayers and point out the analogy between
non-frustrated strongly anisotropic models and frustrated SU(2) ones.Comment: 13 pages, 20 figures; published version with minor change