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 twodimensional 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 \Gamma4 xy . We argue that this is the natural definition of screening in the hierarchical approximation. 1 Introduction In the last ten years the renormalization group ideas have been extensively applied to the two dimensional Coulomb gas of identical charges \Sigmae, in order to rigorously understand the so called Kosterlitz-Thouless phase transition [1]. Associate of the Department of Physics, Harvard University. Supported by Gruppo Nazionale per la Fisica Matematica, CNR, Italy. For inverse temperatures fi larger than the critical one, fi c , and small activity , it has been proved that there is no ..