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We study the high density region of QCD within an effective model obtained inthe frame of the hopping parameter expansion and choosing Polyakov type ofloops as the main dynamical variables representing the fermionic matter. To geta first idea of the phase structure, the model is analyzed in strong couplingexpansion and using a mean field approximation. In numerical simulations, themodel still shows the so-called sign problem, a difficulty peculiar to non-zerochemical potential, but it permits the development of algorithms which ensure agood overlap of the Monte Carlo ensemble with the true one. We review the mainfeatures of the model and present calculations concerning the dependence ofvarious observables on the chemical potential and on the temperature, inparticular of the charge density and the diquark susceptibility, which may beused to characterize the various phases expected at high baryonic density. Weobtain in this way information about the phase structure of the model and thecorresponding phase transitions and cross over regions, which can be consideredas hints for the behaviour of non-zero density QCD.

A Model for QCD at High Density and Large Quark Mass