Renormalization-group flow for the field strength in scalar self-interacting theories

We consider the renormalization-group coupled equations for the effective potential V(ϕ) and the field strength Z(ϕ) in the spontaneously broken phase as a function of the infrared cutoff momentum k. In the k→0 limit, the numerical solution of the coupled equations, while consistent with the expected convexity property of V(ϕ), indicates a sharp peaking of Z(ϕ) close to the end points of the flatness region that define the physical realization of the broken phase. This might represent further evidence in favor of the non-trivial vacuum field renormalization effect already discovered with variational methods.