Abstract
The phase diagram of planar fermionic systems, with four-fermion interactions, are studied when external magnetic fields in different directions are applied to the system. The application of external fields can lead to an asymmetric system, which with the combined effects due to temperature and chemical potential, can lead to a rich phase diagram with multiple critical points. The phase transition we are primarily interested in studying is that of the metal-insulator type, in which our model is particularly well suitable. The relation between the phase transition with chiral symmetry breaking and the emergence of a gap (or the presence of a nonvanishing chiral vacuum expectation value) in the planar fermionic system, as a function of the different magnetic fields applied, is analyzed in details. The applications of our results in the context of condensed matter and quantum field theory at low dimensions are discussed.
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