We study the high density region of QCD within an effective model obtained in the frame of the hopping parameter expansion and choosing Polyakov-type loops as the main dynamical variables representing the fermionic matter. This model still shows the so-called sign problem, a difficulty peculiar to non-zero chemical potential, but it permits the development of algorithms which ensure a good overlap of the simulated Monte Carlo ensemble with the true one. We review the main features of the model and present results concerning the dependence of various observables on the chemical potential and on the temperature, in particular of the charge density and the Polykov loop susceptibility, which may be used to characterize the various phases expected at high baryonic density. In this way, we obtain information about the phase structure of the model and the corresponding phase transitions and cross over regions, which can be considered as hints about the behaviour of non-zero density QCD.
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