N=1 Wess Zumino Model in d=3 at zero and finite temperature

Supersymmetric renormalization group (RG) flow equations for the effective superpotential of the three-dimensional Wess-Zumino model are derived at zero and non-zero temperature. This model with fermions and bosons interacting via a Yukawa term possesses a supersymmetric analogue of the Wilson-Fisher fixed-point. At zero temperature we determine the phase-transition line in coupling-constant space separating the supersymmetric from the non-supersymmetric phase. At finite temperature we encounter dimensional reduction from 3 to 2 dimensions in the infrared regime. We determine the finite-temperature phase diagram for the restoration of the global $Z_2$-symmetry and show that for temperatures above the $Z_2$ phase transition the pressure obeys the Stefan-Boltzmann law of a gas of massless bosons in 2+1 dimensions.