  The QCD phase diagram at finite temperature and density is a topic of
considerable interest. Although much progress has been made in recent years,
some open questions remain. Even at zero density, the order of the transition
for two light flavors of fermions has not yet been conclusively established.
While considerable evidence exists in favor of a second-order transition for
massless quarks and a crossover for massive quarks, some recent results with
two flavors of staggered fermions suggest a transition of first order.
  Since lattice simulations are performed in finite simulation volumes, actual
phase transitions cannot be observed directly. Thus, finite-size scaling is a
very useful tool in the analysis of lattice data. By comparing the scaling
behavior of observables to the expected scaling properties, values of critical
exponents can be confirmed and the order as well as the universality class of a
transition can be established. In the comparison to lattice QCD results, the
critical exponents and the universal scaling functions have been obtained
mainly by means of lattice simulations of O(N) spin models, and results are
usually restricted to the critical temperature or the point at which the
susceptibilities peak.
  We propose to use a non-perturbative Renormalization Group method for this
purpose. We have calculated the critical finite-size scaling behavior and the
universal scaling functions for the three-dimensional O(4)-model for a wide
range of temperatures and values of the symmetry breaking parameter. Our
results are suitable for a comparison to lattice QCD results for the chiral
susceptibility and the order parameter and can be used to check the consistency
of the finite-size scaling behavior with that of the O(N) universality class.
