Lattice artefacts and the running of the coupling constant

Details Lattice artefacts and the running of the coupling constant Lattice artefacts and the running of the coupling constant

2000-09-05

arxiv.org/abs/hep-lat/0009005v2

Phys.Rev. D66 (2002) 034502

Physics

High Energy Physics

High Energy Physics - Lattice

4 pages, 4 figures. To address the criticism that we are studying a different quantitiy than Luscher, Weisz and Wolff original

Scientific paper

10.1103/PhysRevD.66.034502

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.

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