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We calculate the temperature dependent condensate density $\rho^0 (T)$ ofinteracting bosons in three dimensions using the functional renormalizationgroup (FRG). From the numerical solution of suitably truncated FRG flowequations for the irreducible vertices we obtain $\rho^0 (T)$ for arbitrarytemperatures. We carefully extrapolate our numerical results to the criticalpoint and determine the order parameter exponent $\beta \approx 0.32$, inreasonable agreement with the expected value $ 0.345$ associated with theXY-universality class. We also calculate the condensate density in twodimensions at zero temperature using a truncation of the FRG flow equationsbased on the derivative expansion including cubic and quartic terms in theexpansion of the effective potential in powers of the density. As compared withthe widely used quadratic approximation for the effective potential, thecoupling constants associated with the cubic and quartic terms increase theresult for the condensate density by a few percent. However, the cubic andquartic coupling constants flow to rather large values, which sheds some doubton FRG calculations based on a low order polynomial approximation for theeffective potential.

Condensate density of interacting bosons: a functional renormalization group approach