  We study the phase diagram of the two-dimensional N=1 Wess-Zumino model using
Wilson fermions and the fermion loop formulation. We give a complete
non-perturbative determination of the ground state structure in the continuum
and infinite volume limit. We also present a determination of the particle
spectrum in the supersymmetric phase, in the supersymmetry broken phase and
across the supersymmetry breaking phase transition. In the supersymmetry broken
phase we observe the emergence of the Goldstino particle.
