  The sign problem at nonzero chemical potential prohibits the use of
importance sampling in lattice simulations. Since complex Langevin dynamics
does not rely on importance sampling, it provides a potential solution.
Recently it was shown that complex Langevin dynamics fails in the disordered
phase in the case of the three-dimensional XY model, while it appears to work
in the entire phase diagram in the case of the three-dimensional SU(3) spin
model. Here we analyse this difference and argue that it is due to the presence
of the nontrivial Haar measure in the SU(3) case, which has a stabilizing
effect on the complexified dynamics. The freedom to modify and stabilize the
complex Langevin process is discussed in some detail.
