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 gbar(L) = L*m(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.