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.
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