  L\"uscher has suggested a method to determine phase shifts from the finite
volume dependence of the two-particle energy spectrum. We apply this to two
models in d=2: (a) the Ising model, (b) a system of two Ising fields with
different mass and coupled through a 3-point term, both considered in the
symmetric phase. The Monte Carlo simulation makes use of the cluster updating
and reduced variance operator techniques. For the Ising system we study in
particular O($a^2$) effects in the phase shift of the 2-particle scattering
process.
