Improved actions, the perfect action, and scaling by perturbation theory in Wilsons renormalization group: the two dimensional $O(N)$-invariant non linear $\sigma$-model in the hierarchical approximation

C. Wieczerkowski, Y. Xylander

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 r…