  We calculate the temperature dependent condensate density $\rho^0 (T)$ of
interacting bosons in three dimensions using the functional renormalization
group (FRG). From the numerical solution of suitably truncated FRG flow
equations for the irreducible vertices we obtain $\rho^0 (T)$ for arbitrary
temperatures. We carefully extrapolate our numerical results to the critical
point and determine the order parameter exponent $\beta \approx 0.32$, in
reasonable agreement with the expected value $ 0.345$ associated with the
XY-universality class. We also calculate the condensate density in two
dimensions at zero temperature using a truncation of the FRG flow equations
based on the derivative expansion including cubic and quartic terms in the
expansion of the effective potential in powers of the density. As compared with
the widely used quadratic approximation for the effective potential, the
coupling constants associated with the cubic and quartic terms increase the
result for the condensate density by a few percent. However, the cubic and
quartic coupling constants flow to rather large values, which sheds some doubt
on FRG calculations based on a low order polynomial approximation for the
effective potential.
