Renormalization group flow of a hierarchical sine-Gordon model by partial differential equations (Q805921)

We use a renormalization group differential equation to rigorously control the renormalization group flow of a hierarchical lattice Sine- Gordon field theory in the Kosterlitz Thouless phase. As a consequence of an energy estimate, the \(L_ 2\)-norm of the derivative of the effective potential satisfies an exponential upper bound proving that the model is asymptotically free in the infrared limit. More generally, we prove estimates for all derivatives. These estimates provide sufficient information for a detailed analysis of the decay of correlation functions. The method is expected to extend to the full Sine-Gordon model.