Two loop results from the derivative expansion of the blocked action

TL;DR

This paper derives a non-perturbative renormalization group framework for scalar theories using a derivative expansion, enabling the calculation of two-loop anomalous dimensions through polynomial truncation.

Contribution

It introduces a derivative expansion of the Wegner-Houghton equation for scalar theories and demonstrates how to obtain two-loop anomalous dimensions via polynomial truncation.

Findings

Derived non-perturbative RG equations for potential and wave-function renormalization

Showed two-loop anomalous dimension can be obtained from polynomial truncation

Provided a new method to connect non-perturbative RG with perturbative results

Abstract

A derivative expansion of the Wegner-Houghton equation is derived for a scalar theory. The corresponding full non-perturbative renormalization group equations for the potential and the wave-function renormalization function are presented. We also show that the two loop perturbative anomalous dimension for the O(N) theory can be obtained by means of a polynomial truncation in the field dependence in our equations.