  It is argued that universality is severely limited for models with multiple
fixed points. As a demonstration the renormalization group equations are
presented for the potential and the wave function renormalization constants in
the $O(N)$ scalar field theory. Our equations are superior compared with the
usual approach which retains only the contributions that are non-vanishing in
the ultraviolet regime. We find an indication for the existence of relevant
operators at the infrared fixed point, contrary to common expectations. This
result makes the sufficiency of using only renormalizable coupling constants in
parametrizing the long distance phenomena questionable.
