  Nambu-Jona-Lasinio-type models are frequently employed as low-energy models
in various research fields. With respect to the theory of the strong
interaction, this class of models is indeed often used to analyze the structure
of the phase diagram at finite temperature and quark chemical potential. The
predictions from such models for the phase structure at finite quark chemical
potential are of particular interest as this regime is difficult to access with
lattice Monte Carlo approaches. In this work, we consider a Fierz-complete
version of a Nambu-Jona-Lasinio model. By studying its renormalization group
flow, we analyze in detail how Fierz-incomplete approximations affect the
predictive power of such model studies. In particular, we investigate the
curvature of the phase boundary at small chemical potential, the critical value
of the chemical potential above which no spontaneous symmetry breaking occurs,
and the possible interpretation of the underlying dynamics in terms of
difermion-type degrees of freedom. We find that the inclusion of four-fermion
channels other than the conventional scalar-pseudoscalar channel is not only
important at large chemical potential but also leaves a significant imprint on
the dynamics at small chemical potential as measured by the curvature of the
finite-temperature phase boundary.
