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Both in heavy-ion collisions as in magnetars very strong magnetic fields areproduced, which has its influence on the phases of matter involved. In thispaper we investigate the effect of strong magnetic fields (B = 5 m_pi^2 /e =1.7 x 10^19 G) on the chiral symmetry restoring phase transition using theNambu-Jona-Lasinio model. It is observed that the pattern of phase transitionsdepends on the relative magnitude of the magnetic field and the instantoninteraction strength. We study two specific regimes in the phase diagram, highchemical potential and zero temperature and vice versa, which are of relevancefor neutron stars and heavy-ion collisions respectively. In order to shed lighton the behavior of the phase transitions we study the dependence of the minimaof the effective potential on the occupation of Landau levels. We observe anear-degeneracy of multiple minima with differing occupation numbers, of whichsome become the global minimum upon changing the magnetic field or the chemicalpotential. These minima differ considerably in the amount of chiral symmetrybreaking and in some cases also of isospin breaking.

The influence of strong magnetic fields and instantons on the phase structure of the two-flavor NJL model