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

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