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

TL;DR

This paper demonstrates that specific simple lattice actions significantly reduce cutoff effects in 2-d O(N) models, achieving near-continuum accuracy even on coarse lattices, through both numerical and analytical methods.

Contribution

It introduces simple lattice actions that drastically minimize cutoff effects in 2-d O(N) models, improving accuracy on coarse lattices compared to standard actions.

Findings

Cutoff effects reduced to per mille level for step scaling functions

The new actions also minimize cutoff effects for other observables

Analytical insights at N=infinity support numerical results

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.