  The low lying spectrum of the O(n) effective field theory is calculated in
the delta-regime in 3 and 4 space-time dimensions using lattice regularization
to NNL order. It allows, in particular, to determine, using numerical
simulations in different spatial volumes, the pion decay constant F in QCD with
2 flavours or the spin stiffness rho for an antiferromagnet in d=2+1
dimensions.
