  We have studied dimerized spin systems by realizing the cluster expansion to
high order. We have extended our previous dimer expansion for one-dimensional
systems to cover weakly interacting chains for a quantitative description of
three dimensional materials like PHCC and KCuCl_3. By comparison with recent
inelastic neutron scattering data we are able to determine the exchange
energies between individual spins. We have further investigated the
incommensurate region of zigzag chains with isotropic exchange coupling
constants near the disorder-line where the dispersion curve exhibits a minimum
at a finite wavevector. Our approach clearly shows the gradual transition
between the minimum of the dispersion at wavevector 0 and wavevector Pi within
this region. The extent of the incommensurate regime is given analytically in
an expansion in the coupling constants.
