Renormalization group flows into phases with broken symmetry

We describe a method to continue the fermionic renormalization group flow into phases with broken global symmetry. This method does not require a Hubbard-Stratonovich de-coupling of the interaction. Instead an infinitesimally small symmetry-breaking component is inserted into the initial action, as an initial condition for the flow of the self-energy. Its flow is driven by the interaction, and at low scales it saturates at a nonzero value if there is a tendency for spontaneous symmetry breaking in the corresponding channel. For the reduced BCS model, we show how a small initial gap amplitude flows to the value given by the exact solution of the model. We also discuss the emergence of the Goldstone boson in this approach. (author)