Lattice artifacts and the running of the coupling constant

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 16 value used by LWW up to 1 160 . We find much larger lattice artefacts than those 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.

Testing asymptotic scaling and nonabelian symmetry enhancement

“…The choice of the abscissa 1/(ln L + c), was motivated by the fact that in studying lattice artefacts for the LWW step scaling function we found that such an ansatz seemed to describe the data pretty well (see ref. [12] Fig.7). The value of the parameter c = 0.7 was obtained from a joint fit to our O(3) and icosahedron data with a common limiting value for L → ∞; it is of acceptable quality (χ 2 /dof = 11.6/8).…”

“…The choice of the abscissa 1/(ln L + c), was motivated by the fact that in studying lattice artefacts for the LWW step scaling function we found that such an ansatz seemed to describe the data pretty well (see ref. [12] Fig. 7).…”