  We consider a dual representation of an effective three-dimensional Polyakov
loop model for the SU(3) theory at nonzero real chemical potential. This
representation is free of the sign problem and can be used for numeric
Monte-Carlo simulations. These simulations allow us to locate the line of
second order phase transitions, that separates the region of first order phase
transition from the crossover one. The behavior of local observables in
different phases of the model is studied numerically and compared with
predictions of the mean-field analysis. Our dual formulation allows us to study
also Polyakov loop correlation functions. From these results, we extract the
screening masses and compare them with large-N predictions.
