Test of renormalization predictions for universal finite-size scaling functions

We calculate universal finite-size scaling functions for systems with an n- component order parameter and algebraically decaying interactions. Just as previously found for short-range interactions, this leads to a singular eps ilon expansion, where epsilon is the distance to the upper critical dimensi on. Subsequently, we check the results by numerical simulations of spin mod els in the same universality class. Our systems offer the essential advanta ge that epsilon can be varied continuously, allowing an accurate examinatio n of the region where epsilon is small. The numerical calculations turn out to be in striking disagreement with the predicted singularity. [S1063-651X (99)00612-1].