Lattice artefacts and the running of the coupling constant

TL;DR

This study examines the behavior of the LWW coupling constant in the 2D O(3) sigma model, revealing larger lattice artefacts and a slower running than perturbative predictions, highlighting challenges in continuum extrapolation.

Contribution

It provides a detailed analysis of lattice artefacts and the running of the coupling constant at finer lattice spacings, challenging previous perturbative estimates.

Findings

Lattice artefacts are significantly larger than previous estimates.

The coupling runs more slowly than perturbation theory predicts.

Continuum limit extrapolation remains challenging due to uncontrolled artefacts.

Abstract

We study the running of the L\"uscher-Weisz-Wolff (LWW) coupling constant in the two dimensional O(3) nonlinear $\sigma$ model. To investigate the continuum limit we refine the lattice spacing from the $1\over 16$ value used by LWW up to $1\over 160$. We find that the lattice artefacts are much larger than estimated by LWW and that most likely the coupling constant runs slower than predicted by perturbation theory. A precise determination of the running in the continuum limit would require a controlled ansatz of extrapolation, which, we argue, is not presently available.