Previous theories have predicted that O(n) symmetric systems in a finite cubic geometry with periodic boundary conditions have universal finite-size scaling functions near criticality in d>4 dimensions. On the basis of exact results for the O(n) symmetric phi(4) model in the large n limit we show that universal finite-size scaling does not hold in the predicted form because of significant cut-off and lattice effects for d>4. It is shown that finite-size scaling is valid with two reference lengths which turn out to be identical with the amplitudes of the bulk correlation length. For the phi(4) ...
