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Lattice artefacts and the running of the coupling constant

Adrian Patrascioiu·Erhard Seiler
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Abstract

We study the running of the Lüscher-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 $1\over 16$ 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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Adrian Patrascioiu, Erhard Seiler. 2000-11-03. Lattice artefacts and the running of the coupling constant. https://doi.org/10.1103/physrevd.66.034502

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