Magnetic catalysis (and inverse catalysis) at finite temperature in two-color lattice QCD

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Two-color lattice QCD with Nf=4 staggered fermion degrees of freedom (no rooting trick is applied) with equal electric charge q is studied in a homogeneous magnetic background field B and at non-zero temperature T. In order to circumvent renormalization as a function of the bare coupling we apply a fixed-scale approach. We study the influence of the magnetic field on the critical temperature. At rather small pseudo-scalar meson mass (mπ ≈ 175 MeV ≈ Tc(B=0)) we confirm a monotonic rise of the quark condensate <ψ ψ> with increasing magnetic field strength, i.e. magnetic catalysis, as long as one is staying within the confinement or deconfinement phase. In the transition region we find indications for a non-monotonic behavior of Tc(B) at low magnetic field strength (qB<0.8 GeV²) and a clear rise at stronger magnetic field. The conjectured existence of a minimum value Tc(B*) < Tc(B=0) would leave a temperature window for a decrease of <ψ ψ> with rising B (inverse magnetic catalysis) also in the present model.