  Monte Carlo simulations of lattice QCD at non-zero baryon chemical potential
$\mu$ suffer from the notorious complex action problem. We consider QCD with
static quarks coupled to a large chemical potential. This leaves us with an
SU(3) Yang-Mills theory with a complex action containing the Polyakov loop.
Close to the deconfinement phase transition the qualitative features of this
theory, in particular its Z(3) symmetry properties, are captured by the 3-d
3-state Potts model. We solve the complex action problem in the Potts model by
using a cluster algorithm. The improved estimator for the $\mu$-dependent part
of the Boltzmann factor is real and positive and is used for importance
sampling. We localize the critical endpoint of the first order deconfinement
phase transition line and find consistency with universal 3-d Ising behavior.
We also calculate the static quark-quark, quark-anti-quark, and
anti-quark-anti-quark potentials which show screening as expected for a system
with non-zero baryon density.
