Non-Perturbative Renormalization Group for Simple Fluids

We present a new non perturbative renormalization group for classical simple fluids. The theory is built in the Grand Canonical ensemble and in the framework of two equivalent scalar field theories as well. The exact mapping between the three renormalization flows is established rigorously. In the Grand Canonical ensemble the theory may be seen as an extension of the Hierarchical Reference Theory (L. Reatto and A. Parola, Adv. Phys., 44, 211 (1995)) but however does not suffer from its shortcomings at subcritical temperatures. In the framework of a new canonical field theory of liquid state developed in that aim our construction identifies with the effective average action approach developed recently (J. Berges, N. Tetradis, and C. Wetterich, Phys. Rep., 363 (2002)). keywords : Critical Phenomena, Renormalization Group, Theory of Liquids, Hierarchical Reference Theory, Liquid-Vapor Transition, Kac Model. PACS numbers: 05.20.Jj, 05.70.Jk, 11.10.Hi