  We develop several non-perturbative approximations for studying the dynamics
of a supersymmetric O(N) model which preserve supersymmetry. We study the phase
structure of the vacuum in both the leading order in large-N approximation as
well as in the Hartree approximation, and derive the finite temperature
renormalized effective potential. We derive the exact Schwinger-Dyson equations
for the superfield Green functions and develop the machinery for going beyond
the next to leading order in large-N approximation using a truncation of these
equations which can also be derived from a two-particle irreducible effective
action.
