A renormalization group analysis of the Kosterlitz-Thouless phase

We consider a classical Coulomb gas with a short distance cutoff in two dimensions; equivalently a Sine-Gordon field theory. For low temperature β^-1 and low activity z the gas is in a multipole phase, the Kosterlitz-Thouless phase. For β>8π and z sufficiently small we give a complete renormalization group analysis for this phase and show that the flow of the effective measures is toward a free field (infrared asymptotic freedom). This should lead to control over the long distance behavior of the theory.