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The flow equations of the Functional Renormalization Group are applied to theO(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 ofthe 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 physicalrenormalization of the longitudinal component of the field is observed. Thedependence of the field renormalization on the UV cut-off and on the barecoupling is also investigated.

Enhancement of field renormalization in scalar theories via functional renormalization group