  Microscopic models of quantum antiferromagnets are investigated on the basis
of a mapping onto effective low energy hamiltonians. Lattice effects are
carefully taken into account and their role is discussed. We show that the
presence of an external staggered magnetic field modifies in a non trivial way
the usual mapping onto the non linear sigma model, leading to the appearance of
new terms, neglected in previous works. Our analysis is compared with Lanczos
diagonalizations of S=1 Heisenberg chains in a staggered field, confirming the
validity of the single mode approximation for the evaluation of the dynamical
structure factor. The results are relevant for the interpretation of
experiments in quasi-one dimensional compounds. Microscopic realizations of
SU(4) spin chains are also discussed in the framework of spin-orbital lattice
systems. The low energy physics is shown to be described by sigma models with
topological angle $\theta$ in one dimension. This mapping strongly suggests
that the one dimensional CP$^3$ model (with $\theta=\pi$) undergoes a second
order phase transition as a function of the coupling.
