Unexpected results in asymptotically free quantum field theories

We study the behavior of asymptotically free (AF) spin and gauge models whe n their continuous symmetry group is replaced by different discrete non-Abe lian subgroups. Precise numerical results with relative errors down to O(0. 1%) suggest that the models with large subgroups are in the universality cl ass of the underlying original models. We argue that such a scenario is con sistent with the known properties of AF theories. The small statistical err ors allow a detailed investigation of the cut-off effects also. At least up to correlation lengths xi approximate to 300 they follow effectively an cc a rather than the expected proportional to a(2) form both in the O(3) and in the dodecahedron model. (C) 2001 Elsevier Science B.V. All rights reserv ed.