A renormalization group analysis of correlation functions for the dipole gas

We develop a renormalization group method for analyzing the generating functional for charge correlations of a dilute classical dipole gas. It is based on and extends the renormalization group analysis introduced by Brydges and Yau for the dipole gas partition function. Our method leads to systematic formulas for the large-distance behavior of correlation functions of all orders. We prove that in any dimension d≥2, at any value β>0 of the inverse temperature, and at sufficiently small activity z, the correlation functions exhibit at large distances the same behavior as for a vacuum (z=0), but with a new dielectric constant 1+σ over which we have good control. The results proved here extend existing results on the two-point correlations to all higher correlations, and constitute a general confirmation of the fact that dipoles do not screen.