  Both in heavy-ion collisions as in magnetars very strong magnetic fields are
produced, which has its influence on the phases of matter involved. In this
paper 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 the
Nambu-Jona-Lasinio model. It is observed that the pattern of phase transitions
depends on the relative magnitude of the magnetic field and the instanton
interaction strength. We study two specific regimes in the phase diagram, high
chemical potential and zero temperature and vice versa, which are of relevance
for neutron stars and heavy-ion collisions respectively. In order to shed light
on the behavior of the phase transitions we study the dependence of the minima
of the effective potential on the occupation of Landau levels. We observe a
near-degeneracy of multiple minima with differing occupation numbers, of which
some become the global minimum upon changing the magnetic field or the chemical
potential. These minima differ considerably in the amount of chiral symmetry
breaking and in some cases also of isospin breaking.

High Energy Physics - Phenomenology