Average action for the N-component ϕ4 theory

Abstract The average action is a continuum version of the block spin action in lattice field theories. We compute the one-loop approximation to the average potential for the N-component ϕ4 theory in the spontaneously broken phase. For a finite (linear) block size ∼ k −1 this potential is real and nonconvex. For small ϕ the average potential is quadratic, U k = − 1 2 k 2 ϕ 2 , and independent of the original mass parameter and quartic coupling constant. It approaches the convex effective potential as k vanishes.