Mind The Gap

TL;DR

This paper introduces an optimisation criterion based on the inverse effective propagator gap to improve the convergence and reliability of the exact renormalisation group flow calculations, especially for high precision results.

Contribution

It proposes a simple extremisation method of the gap to stabilise the flow and enhance the accuracy of approximate solutions in renormalisation group computations.

Findings

Stabilised the RG flow using the gap extremisation.

Achieved better convergence towards physical theories.

Computed critical exponents for the Ising universality class.

Abstract

We discuss an optimisation criterion for the exact renormalisation group based on the inverse effective propagator, which displays a gap. We show that a simple extremisation of the gap stabilises the flow, leading to better convergence of approximate solutions towards the physical theory. This improves the reliability of truncations, most relevant for any high precision computation. These ideas are closely linked to the removal of a spurious scheme dependence and a minimum sensitivity condition. The issue of predictive power and a link to the Polchinski RG are discussed as well. We illustrate our findings by computing critical exponents for the Ising universality class.