Drastic Reduction of Cutoff Effects in 2-d Lattice O(N) Models

Abstract

We investigate the cutoff effects in 2-d lattice O(N) models for a variety of lattice actions, and we identify a class of very simple actions for which the lattice artifacts are extremely small. One action agrees with the standard action, except that it constrains neighboring spins to a maximal relative angle delta. We fix delta by demanding that a particular value of the step scaling function agrees with its continuum result already on a rather coarse lattice. Remarkably, the cutoff effects of the entire step scaling function are then reduced to the per mille level. This also applies to the theta-vacuum effects of the step scaling function in the 2-d O(3) model. The cutoff effects of other physical observables including the renormalized coupling and the mass in the isotensor channel are also reduced drastically. Another choice, the mixed action, which combines the standard quadratic with an appropriately tuned large quartic term, also has extremely small cutoff effects. The size of cutoff effects is also investigated analytically in 1-d and at N = infinity in 2-d.

39 pages, 18 figures

References in corpus (5)

• The puzzle of apparent linear lattice artifacts in the 2d non-linear sigma-model and Symanzik's solution
• Topological Lattice Actions
• Logarithmic corrections to O(a^2) lattice artifacts
• Non-trivial θ-Vacuum Effects in the 2-d O(3) Model
• An ideal toy model for confining, walking and conformal gauge theories: the O(3) sigma model with theta-term

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• Asymptotic low-temperature behavior of two-dimensional RP${}^{N-1}$ models
• An Improved Single-Plaquette Gauge Action
• The universal coefficient of the exact correlator of a large-$N$ matrix field theory
• Symanzik effective actions in the large N limit