High-accuracy scaling exponents in the local potential approximation

TL;DR

This paper compares different formulations of Wilson's renormalisation group by computing critical exponents and fixed point potentials for the Ising model, achieving high numerical accuracy and revealing subtle differences.

Contribution

It demonstrates numerical equivalence of Wilson-Polchinski and optimized RG flows with unprecedented precision, and contrasts these with Dyson's hierarchical model results.

Findings

Wilson-Polchinski and optimized RG flows are numerically equivalent.

Small but systematic differences exist between RG methods and Dyson's model.

High-accuracy computation of scaling exponents and fixed point potentials.

Abstract

We test equivalences between different realisations of Wilson's renormalisation group by computing the leading, subleading, and anti-symmetric corrections-to-scaling exponents, and the full fixed point potential for the Ising universality class to leading order in a derivative expansion. We discuss our methods with a special emphasis on accuracy and reliability. We establish numerical equivalence of Wilson-Polchinski flows and optimised renormalisation group flows with an unprecedented accuracy in the scaling exponents. Our results are contrasted with high-accuracy findings from Dyson's hierarchical model, where a tiny but systematic difference in all scaling exponents is established. Further applications for our numerical methods are briefly indicated.