Logarithmic corrections to O(a^2) lattice artifacts

Abstract

We compute logarithmic corrections to the O(a^2) lattice artifacts for a class of lattice actions for the non-linear O(n) sigma-model in two dimensions. The generic leading artifacts are of the form $a^2[\ln (a^2){]}^{(n/(n-2))}$. We also compute the next-to-leading corrections and show that for the case n=3 the resulting expressions describe well the lattice artifacts in the step scaling function, which are in a large range of the cutoff apparently of the form O(a). An analogous computation should, if technically possible, accompany any precision measurements in lattice QCD.

13 pages, 3 figures

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• TBA equations for excited states in the O(3) and O(4) nonlinear $\sigma$-model
• Lattice 2001: Reflections
• Nonstandard Cutoff Effects in the Nonlinear Sigma Model
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