  We have simulated the asymptotically free two-dimensional O(3) model at
nonzero chemical potential using the model's dual representation. We first
demonstrate how the latter solves the sign (complex action) problem. The system
displays a crossover at nonzero temperature, while at zero temperature it
undergoes a quantum phase transition when mu reaches the particle mass
(generated dynamically similar to QCD). The density follows a square root
behavior universal for repulsive bosons in one spatial dimension. We have also
measured the spin stiffness, known to be sensitive to the spatial correlation
length, using different scaling trajectories to zero temperature and infinite
size. It points to a dynamical critical exponent z=2. Comparisons to
thermodynamic Bethe ansaetze are shown as well.
