| Summary: | 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.
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