  Variational wave functions containing electronic pairing and suppressed
charge fluctuations (i.e., projected BCS states) have been proposed as the
paradigm for disordered magnetic systems (including spin liquids). Here we
discuss the general properties of these states in one and two dimensions, and
show that different quantum phases may be described with high accuracy by the
same class of variational wave functions, including dimerized and magnetically
ordered states. In particular, phases with magnetic order may be obtained from
a straightforward generalization containing both antiferromagnetic and
superconducting order parameters, as well as suitable spin Jastrow
correlations. In summary, projected wave functions represent an extremely
flexible tool for understanding the physics of low-dimensional magnetic
systems.
