Lattice artefacts and the running of the coupling constant
Abstract
We study the running of the L\"uscher-Weisz-Wolff (LWW) coupling constant in the two dimensional O(3) nonlinear σ model. To investigate the continuum limit we refine the lattice spacing from the 1 16 value used by LWW up to 1 160. 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.
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