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

Comparison of complex Langevin and mean field methods applied to effective Polyakov line models