Scaling and superscaling solutions from the functional renormalization group

We study the renormalization group flow of Z2-invariant supersymmetric and nonsupersymmetric scalar models in the local potential approximation using functional renormalization group methods. We focus our attention on the fixed points of the renormalization group flow of these models, which emerge as scaling solutions. In two dimensions these solutions are interpreted as the minimal (supersymmetric) models of conformal field theory, while in three dimensions they are manifestations of the Wilson-Fisher universality class and its supersymmetric counterpart. We also study the analytically continued flow in fractal dimensions between 2 and 4 and determine the critical dimensions for which irrelevant operators become relevant and change the universality class of the scaling solution. We include novel analytic and numerical investigations of the properties that determine the occurrence of the scaling solutions within the method. For each solution we offer new techniques to compute the spectrum of the deformations and obtain the corresponding critical exponents.