Fermionic functional renormalization-group for first-order phase transitions: a mean-field model

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.