Laboratoire de Physique Théorique
Toulouse - UMR 5152

The renormalization group (RG) has been introduced in its modern form by Wilson in the seventies, based on the concept of block spin of Kadanoff. Although nonperturbative in essence the RG has been, for a long time, confined to the perturbative domain : small coupling constant, small disorder, vicinity of the upper or lower critical dimension, etc

In the nineties, Wetterich has introduced a new formulation of the NPRG, based on the concept of running free energy. This formulation turns out to be the most suitable one to tackle with nonperturbative issues : strong coupling behaviour, physics far from the upper or lower critical dimensions, effects of topological excitations, of bound states, of disorder, etc

I first present the general principles of the method. Then I illustrate these principles with different examples coming from condensed matter physics.