Derivative expansion of the renormalization group in O(N) scalar field theory

TL;DR

This paper applies a derivative expansion to the renormalization group equations in O(N) scalar field theory, accurately computing critical exponents and reproducing known results at specific N values.

Contribution

It introduces a derivative expansion method to the RG flow equations without additional approximations, calculating critical exponents for various N.

Findings

Calculated critical exponents eta, nu, omega at different N values

Reproduced known results exactly at N=infinity, -2, -4, ...

Validated the derivative expansion approach for O(N) theories

Abstract

We apply a derivative expansion to the Legendre effective action flow equations of O(N) symmetric scalar field theory, making no other approximation. We calculate the critical exponents eta, nu, and omega at the both the leading and second order of the expansion, associated to the three dimensional Wilson-Fisher fixed points, at various values of N. In addition, we show how the derivative expansion reproduces exactly known results, at special values N=infinity,-2,-4, ... .