  The flow equations of the Functional Renormalization Group are applied to the
O(N)-symmetric scalar theory, for N=1 and N=4, in four Euclidean dimensions,
d=4, to determine the effective potential and the renormalization function of
the field in the broken phase. In our numerical analysis, the infrared limit,
corresponding to the vanishing of the running momentum scale in the equations,
is approached to obtain the physical values of the parameters by extrapolation.
In the N=4 theory a non-perturbatively large value of the physical
renormalization of the longitudinal component of the field is observed. The
dependence of the field renormalization on the UV cut-off and on the bare
coupling is also investigated.
