  We calculate within a mean-field approximation the slopes of the critical
lines near the point of appearing the ferrimagnetic phase for the U(1) systems
in the weak coupling regime. It is demonstrated that the slope of one of the
critical line is continuous, while change of the slope of the other depends
strongly on the number of the fermion flavours. We also find that in the
ferrimagnetic phase near such a point the magnetization and the staggered
magnetization align orthogonally to each other.
