Non-perturbative renormalization group for simple fluids

Abstract

We present a new non-perturbative renormalization group for classical simple fluids. The theory is built in the Grand Canonical ensemble and also in the framework of two equivalent scalar field theories. 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 [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 for the liquid state developed with that aim, our construction identifies with the effective average action approach developed recently [Phys. Rep. 363 (2002)].

Keywords:

• Critical phenomena
• Renormalization group
• Theory of liquids
• Hierarchical Reference Theory
• Liquid–vapour transition
• Kac model

Acknowledgements

I attended the lectures of B. Delamotte on the NPRG in spring 2005 at Jussieu University (Paris, France), which was a marvelous introduction to the subject. The interested reader is urged to consult his lecture notes which are available on the Web 9. I acknowledge the anonymous referee for interesting remarks on the manuscript and A. Reiner for valuable e-mail correspondence.