  We extend the critical point self-consistency method used to solve field
theories at their d-dimensional fixed point in the large N expansion to include
superfields. As an application we compute the beta-function of the Wess-Zumino
model with an O(N) symmetry to O(1/N^2). This result is then used to study the
effect the higher order corrections have on the radius of convergence of the
4-dimensional beta-function at this order in 1/N. The critical exponent
relating to the wave function renormalization of the basic field is also
computed to O(1/N^2) and is shown to be the same as that for the corresponding
field in the supersymmetric O(N) sigma model in d-dimensions. We discuss how
the non-renormalization theorem prevents the full critical point equivalence
between both models.
