Can numerics on small lattices reveal the true continuum limit?

Using ideas of finite size scaling, we apply a recently discovered criterion to some published lattice data to test how close they are to the continuum limit. We find that these data show large lattice artefacts. In addition we find that data that are supposed to determine the running of a renormalized coupling constant suggest a very slow (logarithmic) approach to the continuum limit; taking this into account we find that the physical coupling runs more slowly than the perturbative β function predicts, in agreement with the existence of a critical point at non-zero coupling.