Subleading critical exponents from the renormalisation group

TL;DR

This paper uses exact renormalisation group equations to accurately compute correction-to-scaling exponents in the 3d Ising universality class, revealing that antisymmetric corrections are significantly subleading.

Contribution

It provides high-precision calculations of symmetric and antisymmetric correction-to-scaling exponents using various cutoff schemes within the renormalisation group framework.

Findings

Antisymmetric corrections are strongly subleading compared to symmetric ones.

Results are consistent across different cutoff schemes.

Estimate for higher order correction contributions.

Abstract

We study exact renormalisation group equations for the 3d Ising universality class. At the Wilson-Fisher fixed point, symmetric and antisymmetric correction-to-scaling exponents are computed with high accuracy for an optimised cutoff to leading order in the derivative expansion. Further results are derived for other cutoffs including smooth, sharp and background field cutoffs. An estimate for higher order corrections is given as well. We establish that the leading antisymmetric corrections to scaling are strongly subleading compared to the leading symmetric ones.