  First-order phase transitions in many-fermion systems are not detected in the
susceptibility analysis of common renormalization-group (RG) approaches. Here
we introduce a counterterm technique within the functional
renormalization-group (fRG) formalism which allows access to all stable and
metastable configurations. It becomes possible to study symmetry-broken states
which occur through first-order transitions as well as hysteresis phenomena.
For continuous transitions, the standard results are reproduced. As an example,
we study discrete-symmetry breaking in a mean-field model for a commensurate
charge-density wave. An additional benefit of the approach is that away from
the critical temperature for the breaking of discrete symmetries large
interactions can be avoided at all RG scales.
