  We propose an interaction flow scheme that sums up the perturbation expansion
of many-particle systems by successively increasing the interaction strength.
It combines the unbiasedness of renormalization group methods with the
simplicity of straight-forward perturbation theory. Applying the scheme to
fermions in one dimension and to the two-dimensional Hubbard model we find that
at one-loop level and low temperatures there is ample agreement with previous
one-loop renormalization group approaches. We furthermore present results for
the momentum-dependence of spin, charge and pairing interactions in the
two-dimensional Hubbard model.
