Nontrivial fixed points and screening in the hierarchical two-dimensional Coulomb gas.

We show the existence and asymptotic stability of two fixed points of the renormalization group transformation for the hierarchical two-dimensional Coulomb gas in the sine-Gordon representation and temperatures slightly greater than the critical one. We prove also that the correlations at the fixed points decay as in the hierarchical massive scalar free field theory, that is as $d_{xy}^{-4}$. We argue that this is the natural definition of screening in the hierarchical approximation