  We discuss spontaneous supersymmetry breaking in the N=1 Wess-Zumino model in
two dimensions on the lattice using Wilson fermions and the fermion loop
formulation. In that formulation the fermion sign problem related to the
vanishing of the Witten index can be circumvented and the model can be
simulated very efficiently using the recently introduced open fermion string
algorithm. We present first results for the supersymmetry breaking phase
transition and sketch the preliminary determination of a renormalised critical
coupling in the continuum limit.
