Finite-size-scaling functions for 3d O (4) and O (2) spin models and QCD

We calculate numerically universal finite-size-scaling functions for the th ree-dimensional O(4) and O(2) models. The approach of these functions to th e infinite-volume scaling functions is studied in detail on the critical an d pseudocritical lines. For this purpose we determine the pseudocritical li ne in two different ways. We find that the asymptotic form of the finite-si ze-scaling functions is already reached at small values of the scaling vari able. A comparison with QCD lattice data for two flavours of staggered ferm ions shows a similar finite-size behaviour which is compatible with that of the spin models. (C) 2001 Elsevier Science B.V. All rights reserved.