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.