  In this study, we investigate the Nambu--Jona-Lasinio (NJL) model at finite
temperature and finite density in an external magnetic field using the
functional renormalization group. We investigate the dependence of the position
of the ultraviolet fixed point (UVFP) of the four-Fermi coupling constant on
the temperature, density, and external magnetic field, and we obtain the chiral
phase structure. The UVFP at low temperature and finite chemical potential
oscillates in a small external magnetic field, which can be interpreted as the
de Haas--van Alphen effect. We also obtain phase diagrams with complex
structures, where the phase boundary moves back and forth as the external
magnetic field increases in the low temperature and high density region.
