  We compute the free energy of helium-4 near the lambda transition based on an
exact renormalization-group equation. An approximate solution permits the
determination of universal and nonuniversal thermodynamic properties starting
from the microphysics of the two-particle interactions. The method does not
suffer from infrared divergences. The critical chemical potential agrees with
experiment. This supports a specific formulation of the functional integral
that we have proposed recently. Our results for the equation of state reproduce
the observed qualitative behavior. Despite certain quantitative shortcomings of
our approximation, this demonstrates that ab initio calculations for collective
phenomena become possible by modern renormalization-group methods.
