Lattice artefacts and the running of the coupling constant
@article{Patrascioiu2002LatticeAA,
title={Lattice artefacts and the running of the coupling constant},
author={Adrian Patrascioiu and Erhard Seiler},
journal={Physical Review D},
year={2002},
volume={66}
}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…