Long Range Ferromagnets: Renormalization Group Analysis
Abstract
In this lecture I will first review rigorous results in the theory of ferromagnets with continuous spins and long range interactions on a lattice. In the long wave length approximation we get a lattice field theory of continuous spins with a non-linear perturbation.
I will then give a rigorous version of Wilson's renormalisation group to take the continuum limit as a scaling limit in a finite volume. We construct a critical theory which has a non trivial fixed point. Moreover we prove the existence of correlation functions and obtain the true scaling dimension of fields.