The renormalization group improved effective potential in massless models

The effective potential V is considered in massless lambda phi(4)(4) theory. The expansion of V in powers of the coupling lambda and of the logarithm of the. background field is reorganized in two ways; first as a series in a alone, then as a series in In (0 alone. By applying the renormalization group (RG) equation to V, these expansions can be summed. Using the condition V'(v) = 0 (where v is the vacuum expectation value of phi) in conjunction with the expansion of V in powers of In fixes V provided v not equal 0. In this case, the dependence of V on phi drops out and V is not analytic in lambda. Massless scalar electrodynamics is considered using the same approach.