Nonperturbative approach of the principal chiral model between two and four dimensions

We investigate the principal chiral model between two and four dimensions b y means of a nonperturbative Wilson-like renormalization-group equation. We are thus able to follow the evolution of the effective coupling constants within this whole range of dimensions without having recourse to any kind o f small parameter expansion. This allows us to identify its three-dimension al critical physics and to solve the long-standing discrepancy between the different perturbative approaches that characterizes the class of models to which the principal chiral model belongs.