  A non-perturbative Renormalization Group approach is used to calculate
scaling functions for an O(4) model in d=3 dimensions in the presence of an
external symmetry-breaking field. These scaling functions are important for the
analysis of critical behavior in the O(4) universality class. For example, the
finite-temperature phase transition in QCD with two flavors is expected to fall
into this class. Critical exponents are calculated in local potential
approximation. Parameterizations of the scaling functions for the order
parameter and for the longitudinal susceptibility are given. Relations from
universal scaling arguments between these scaling functions are investigated
and confirmed. The expected asymptotic behavior of the scaling functions
predicted by Griffiths is observed. Corrections to the scaling behavior at
large values of the external field are studied qualitatively. These scaling
corrections can become large, which might have implications for the scaling
analysis of lattice QCD results.
