Lattice artefacts and the running of the coupling constant

  title={Lattice artefacts and the running of the coupling constant},
  author={Adrian Patrascioiu and Erhard Seiler},
  journal={Physical Review D},
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… 
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