PUB - Publikationen an der Universität Bielefeld

We present direct representations of the scaling functions of the 3d O(4)model which are relevant for comparisons to other models, in particular QCD.This is done in terms of expansions in the scaling variablez=t/h^{1/\beta\delta}. The expansions around z=0 and the correspondingasymptotic ones for z --> +/- infty, overlap such that no interpolation isneeded. We explicitly present the expansion coefficients which have beendetermined numerically from data of a previous high statistics simulation ofthe O(4) model on a three-dimensional lattice of linear extension L=120. Thisallows to derive smooth representations of the first three derivatives of thescaling function of the free energy density, which determine universalproperties of up to sixth order cumulants of net charge fluctuations in QCD.