We study the behavior of strongly interacting matter under a strong external magnetic field in the context of chiral quark models that include nonlocal interactions. In particular, we analyze the influence of a constant magnetic field on the chiral quark condensates at zero and finite temperature, studying the deconfinement and chiral restoration critical temperatures and discussing the observed magnetic catalysis and inverse magnetic catalysis effects. In addition, we analyze in this framework the behavior of the $pi^0$ mass and decay constant. The predictions of nonlocal chiral quark models are compared with results obtained in lattice QCD.
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