Convergence and stability of the renormalisation group

TL;DR

This paper investigates how the choice of regulator affects the stability and convergence of the renormalisation group flow, demonstrating that optimized regularisation improves flow properties with implications for various theories.

Contribution

It shows that stability and convergence in the exact renormalisation group depend on regulator choice, highlighting optimized regularisation as a key factor.

Findings

Stability properties are controlled by regulator choice.

Optimized regularisation enhances flow convergence.

Illustration with 3d scalar theories at criticality.

Abstract

Within the exact renormalisation group approach, it is shown that stability properties of the flow are controlled by the choice for the regulator. Equally, the convergence of the flow is enhanced for specific optimised choices for the regularisation. As an illustration, we exemplify our reasoning for 3d scalar theories at criticality. Implications for other theories are discussed.