Lattice study of RG fixed point based on gradient flow in $3$D $O(N)$ sigma model

TL;DR

This paper uses lattice simulations and gradient flow techniques to non-perturbatively analyze the renormalization group flow and confirm the Wilson--Fisher fixed point in the 3D $O(N)$ sigma model.

Contribution

It introduces a novel approach to study RG flow using gradient flow on the lattice, confirming the fixed point beyond perturbation theory.

Findings

Confirmation of the Wilson--Fisher fixed point non-perturbatively

Demonstration of the scaling behavior via gradient flow

Numerical evidence supporting RG flow analysis in finite N

Abstract

We present the lattice simulation of the renormalization group flow in the $3$-dimensional $O(N)$ linear sigma model. This model possesses a nontrivial infrared fixed point, called Wilson--Fisher fixed point. Arguing that the parameter space of running coupling constants can be spanned by expectation values of operators evolved by the gradient flow, we exemplify a scaling behavior analysis based on the gradient flow in the large $N$ approximation at criticality. Then, we work out the numerical simulation of the theory with finite $N$. Depicting the renormalization group flow along the gradient flow, we confirm the existence of the Wilson--Fisher fixed point non-perturbatively.