Three dimensional massive scalar field theory and the derivative expansion of the renormalization group

TL;DR

This paper demonstrates a continuum approach to determine non-perturbative fixed points and universal couplings in three-dimensional scalar field theories using a derivative expansion, achieving results comparable to other advanced methods.

Contribution

It introduces a continuum method to directly compute fixed points and couplings in scalar field theories without bare actions or tuning, using a derivative expansion.

Findings

Estimated universal couplings in the 3D Ising universality class.

Achieved close agreement with other methods for most couplings.

Provided new estimates for high-order n-point couplings at zero momentum.

Abstract

We show that non-perturbative fixed points of the exact renormalization group, their perturbations and corresponding massive field theories can all be determined directly in the continuum -- without using bare actions or any tuning procedure. As an example, we estimate the universal couplings of the non-perturbative three-dimensional one-component massive scalar field theory in the Ising model universality class, by using a derivative expansion (and no other approximation). These are compared to the recent results from other methods. At order derivative-squared approximation, the four-point coupling at zero momentum is better determined by other methods, but factoring this out appropriately, all our other results are in very close agreement with the most powerful of these methods. In addition we provide for the first time, estimates of the n-point couplings at zero momentum, with n=12,14, and the order momentum-squared parts with n=2 ... 10.