Abstract:
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.