Improved actions, the perfect action, and scaling by perturbation theory in Wilson's renormalization group: the two-dimensional O( N)-invariant non-linear σ-model in the hierarchical approximation

Abstract

We propose a method using perturbation theory in the running coupling constant and the idea of scaling to determine improved actions for lattice field theories combining Wilson's renormalization group with Symanzik's improvement program. The method is based on the analysis of a single renormalization group transformation. We test it on the hierarchical O( N)-invariant σ-model in two dimensions.