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 ɛ expansion, where ɛ is the distance to the upper critical dimension. Subsequently, we check the results by numerical simulations of spin models in the same universality class. Our systems offer the essential advantage that ɛ can be varied continuously, allowing an accurate examination of the region where ɛ is small. The numerical calculations turn out to be in striking disagreement with the predicted singularity.