  The influence of the magnetic field on the pion superfluidity and the phase
structure is analyzed in the framework of the two-flavor
Nambu--Jona-Lasinio(NJL) model. To do this, we first derive the thermodynamic
potential from the Lagrangian density of the NJL model in the mean field
approximation. Using this thermodynamic potential, we get the gap equation of
the chiral condensate and the pion condensate. The effect of external magnetic
field on the pion condensate is not simple promotion or suppression, which we
will discuss in detail in the paper. It is shown that the tricritical point on
the pion superfluidity phase transition line moves to the space with smaller
isospin chemical potential and higher temperature when the external magnetic
field becomes stronger. The influence of external magnetic field on the chiral
condensate is also studied.
