  We analyse supersymmetric models that show supersymmetry breaking in one and
two dimensions using lattice methods. Starting from supersymmetric quantum
mechanics we explain the fundamental principles and problems that arise in
putting supersymmetric models onto the lattice. We compare our lattice results
(built upon the non-local SLAC derivative) with numerically exact results
obtained within the Hamiltonian approach. A particular emphasis is put on the
discussion of boundary conditions. We investigate the ground state structure,
mass spectrum, effective potential and Ward identities and conclude that
lattice methods are suitable to derive the physical properties of
supersymmetric quantum mechanics, even with broken supersymmetry. Based on this
result we analyse the two dimensional N=1 Wess-Zumino model with spontaneous
supersymmetry breaking. First we show that (in agreement with earlier
analytical and numerical studies) the SLAC derivative is a sensible choice in
the quenched model, which is nothing but the two dimensional phi^4 model. Then,
we present the very first computation of a renormalised critical coupling for
the complete supersymmetric model. This calculation makes use of Binder
cumulants and is supported by a direct comparison to Ward identity results,
both in the continuum and infinite volume limit. The physical picture is
completed by masses at two selected couplings, one in the supersymmetric phase
and one in the supersymmetry broken phase. Signatures of the Goldstino in the
fermionic correlator are clearly visible in the broken case.
