  We show that for a $\lambda\phi^4$ theory having many components, the
solution with all equal components in the infrared regime is stable with
respect to our expansion given by a recently devised approach to analyze
strongly coupled quantum field theory. The analysis is extended to a pure
Yang-Mills theory showing how, in this case, the given asymptotic series
exists. In this way, many components theories in the infrared regime can be
mapped to a single component scalar field theory obtaining their spectrum.
