Enhancement of field renormalization in scalar theories via functional renormalization group

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 nonperturbatively large value of the physical renormalization of the longitudinal component of the field is observed. The dependence of the field renormalization on the UV cutoff and on the bare coupling is also investigated.