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

Abstract 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.