  It has been demonstrated that the effective potential V(\phi) in a massless
O(N) \lambda \phi^4_4 model is determined completely by the renormalization
group functions provided the renormalization condition \frac{d^4V}{d
\phi^4}|_{\phi=\mu}=\lambda is used. This is shown to also hold in massless
scalar electrodynamics. By employing a variant of the method of
characteristics, the sums contributing to the leading-log, next-to-leading-log
etc. contributions to V(\phi) can be evaluated.
