Cutoff Effects in O(N) Nonlinear Sigma Models

Abstract

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.

23 pages, 13 Figures, minor changes for clarification

References in corpus (7)

• First results on the running coupling in QCD with two massless flavours
• Corrections to Finite-Size Scaling in the Lattice N-Vector Model for Infinite N
• TBA equations for excited states in the O(3) and O(4) nonlinear $\sigma$-model
• Correction to four-loop RG functions in the two-dimensional lattice O(n) $\sigma$-model
• Unexpected results in asymptotically free quantum field theories
• Nonstandard Cutoff Effects in the Nonlinear Sigma Model
• An Improved Estimator for the Correlation Function of 2D Nonlinear Sigma Models

Cited by in corpus (7)

• The puzzle of apparent linear lattice artifacts in the 2d non-linear sigma-model and Symanzik's solution
• Asymptotic behavior of cutoff effects in Yang-Mills theory and in Wilson's lattice QCD
• Logarithmic corrections to O(a^2) lattice artifacts
• Non-trivial θ-Vacuum Effects in the 2-d O(3) Model
• Drastic Reduction of Cutoff Effects in 2-d Lattice O(N) Models
• An Improved Single-Plaquette Gauge Action
• Cutoff effects in the O(N) sigma model at large N