  We solve analytically the renormalization-group equation for the potential of
the O(N)-symmetric scalar theory in the large-N limit and in dimensions 2<d<4,
in order to look for nonperturbative fixed points that were found numerically
in a recent study. We find new real solutions with singularities in the higher
derivatives of the potential at its minimum, and complex solutions with branch
cuts along the negative real axis.
