  We study the effect of an external magnetic field on the chiral phase
transition in the theory of the strong interaction by means of a
renormalization-group (RG) fixed-point analysis, relying on only one physical
input parameter, the strong coupling at a given large momentum scale. To be
specific, we consider the interplay of the RG flow of four-quark interactions
and the running gauge coupling. Depending on the temperature and the strength
of the magnetic field, the gauge coupling can drive the quark sector to
criticality, resulting in chiral symmetry breaking. In accordance with lattice
Monte-Carlo simulations, we find that the chiral phase transition temperature
decreases for small values of the external magnetic field. For large magnetic
field strengths, however, our fixed-point study predicts that the phase
transition temperature increases monotonically.
