  Higher order quantum effects on the magnetic phase diagram induced by
four-spin ring exchange on plaquettes are investigated for a two-dimensional
quantum antiferromagnet with S=1/2. Spatial anisotropy and frustration are
allowed for. Using a perturbative spin-wave expansion up to second order in 1/S
we obtain the spin-wave energy dispersion, sublattice magnetization, and the
magnetic phase diagram. We find that for substantial four-spin ring exchange
the quantum fluctuations are stronger than in the standard Heisenberg model. A
moderate amount of four-spin ring exchange couplings stabilizes the ordered
antiferromagnetic Neel state while a large amount renders it unstable.
Comparison with inelastic neutron scattering data points toward a moderate ring
exchange coupling of 27% to 29% of the nearest-neighbor exchange coupling.
