Cutoff Effects in O(N) Nonlinear Sigma Models

Details Cutoff Effects in O(N) Nonlinear Sigma Models Cutoff Effects in O(N) Nonlinear Sigma Models

2005-06-09

arxiv.org/abs/hep-lat/0506010v2

Nucl.Phys. B726 (2005) 421-440

Physics

High Energy Physics

High Energy Physics - Lattice

23 pages, 13 Figures, minor changes for clarification

Scientific paper

10.1016/j.nuclphysb.2005.08.002

In the nonlinear O(N) sigma model at N=3 unexpected cutoff effects have been found before with standard discretizations and lattice spacings. Here the situation is analyzed further employing additional data for the step scaling function of the finite volume massgap at N=3,4,8 and a large N-study of the leading as well as next-to-leading terms in 1/N. The latter exact results are demonstrated to follow Symanzik's form of the asymptotic cutoff dependence. At the same time, when fuzzed with artificial statistical errors and then fitted like the Monte Carlo results, a picture similar to N=3 emerges. We hence cannot conclude a truly anomalous cutoff dependence but only relatively large cutoff effects, where the logarithmic component is important. Their size shrinks at larger N, but the structure remains similar. The large N results are particularly interesting as we here have exact nonperturbative control over an asymptotically free model both in the continuum limit and on the lattice.

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