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Using the renormalization group techniques it was previously shown that the perturbative effective potential in the $\mathcal{O}(N)$ symmetric $\phi^4$ theory, massless scalar electrodynamics as well as in the conformal limit of the standard model can be uniquely determined in terms of the known MS scheme renormalization group functions. Furthermore, re-summation of the leading order corrections plus portions of these higher order contributions to the effective potential in the $\mathcal{O}(N)$ symmetric $\phi^4$ theory shows a peculiar shift in the usual "Landau singularity" apparent in the individual leading order corrections. In this work, we have further investigated this shift by extending the result for theories having multiple couplings. We have shown that the singularity structure of the effective potential as seen by summing up portions of the $V_{N^{P+n}LL}$ for any finite $P$ is altered as expected when these perturbative contributions are summed to all orders but more significantly we found that this shift in the singularity is completely determined by the one and two loop beta functions only. We argue that this is a general result which applies to the conformally invariant standard model., Comment: 25 pages, added reference, typos corrected

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., Comment: Results of this work are now combined with findings in arXiv:0706.1760. These results will appear in Phys. Rev. D 77, 065007 (2008). As a result, this manuscript is being withdrawn