  We present lattice results for simulations of the $O(3)$ non-linear sigma
model at finite chemical potential. The complex action problem is overcome by a
dual variable representation of the model. We discuss two aspects of the theory
at finite density: 1) The relation of the finite density data to scattering
phases and wave-functions. 2) The phase-structure of the theory as a function
of chemical potential and the possibility of a Kosterlitz-Thouless phase
transition.
