  We derive a supersymmetric renormalization group (RG) equation for the
scale-dependent superpotential of the supersymmetric O(N) model in three
dimensions. For a supersymmetric optimized regulator function we solve the RG
equation for the superpotential exactly in the large-N limit. The fixed-point
solutions are classified by an exactly marginal coupling. In the weakly coupled
regime there exists a unique fixed point solution, for intermediate couplings
we find two separate fixed point solutions and in the strong coupling regime no
globally defined fixed-point potentials exist. We determine the exact critical
exponents both for the superpotential and the associated scalar potential.
Finally we relate the high-temperature limit of the four-dimensional theory to
the Wilson-Fisher fixed point of the purely scalar theory.
