  Effective Polyakov line models, derived from SU(3) gauge-matter systems at
finite chemical potential, have a sign problem. In this article I solve two
such models, derived from SU(3) gauge-Higgs and heavy quark theories by the
relative weights method, over a range of chemical potentials where the sign
problem is severe. Two values of the gauge-Higgs coupling are considered,
corresponding to a heavier and a lighter scalar particle. Each model is solved
via the complex Langevin method, following the approach of Aarts and James, and
also by a mean field technique. It is shown that where the results of mean
field and complex Langevin agree, they agree almost perfectly. Where the
results of the two methods diverge, it is found that the complex Langevin
evolution has a branch cut crossing problem, associated with a logarithm in the
action, that was pointed out by Mollgaard and Splittorff.
