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I introduce an approximation scheme that allows to deduce differentialequations for the renormalization group $\beta$-function from aSchwinger--Dyson equation for the propagator. This approximation is proven togive the dominant asymptotic behavior of the perturbative solution. In thesupersymmetric Wess--Zumino model and a $\phi^3_6$ scalar model which do nothave divergent vertex functions, this simple Schwinger--Dyson equation for thepropagator captures the main quantum corrections.

Approximate Differential Equations for Renormalization Group Functions in Models Free of Vertex Divergencies