Nonstandard cutoff effects in the nonlinear sigma model

High precision measurements of the renormalized zero-momentum 4-point coupling g(R) and of the Luscher-Weisz-Wolff running coupling (g) over bar (L) = Lm(L) performed with two different lattice actions in the non-perturbative region confirm the earlier observations, that the cutoff effects look linear, in contrast to perturbative considerations. The use of different actions allows one to make a more reliable estimate on the continuum limit. The measurements were done for infinite volume correlation length up to 350.