Renormalization group and quantum critical phenomena in the large-n limit

The paper is devoted to a sistematic study of the critical behaviour and quantum regime of a wide class of quantum systems on the basis of the Renormalization Group (RG) approach in the large-n limit. It can be considered as a complement to recent perturbative (RG) investigations for the same systems and as a convenient basis for a treatment of the classical-quantum crossover. The differences between “Bosonized systems” and several quantum systems for which a dimensional crossover occurs in the low temperature limit are emphasized, consistently with the perturbative results and a calculation of the quantum non linear scaling field is also realized. Finally, a differential formulation of the quantum RG in the large-n limit is presented and its convenience in investigating some aspects of the problem is pointed out.