  Using the determinant quantum Monte Carlo method, we investigate the
antiferromagnetic phase transition that is induced by the Zeeman field in a
disordered interacting two-dimensional Dirac fermion system. At a fixed
interaction strength $U$, the antiferromagnetic correlation is enhanced as the
magnetic filed increases, and when the magnetic field is larger than a
$B_{c}(U)$, the antiferromagnetic correlation shall be suppressed by the
increased magnetic field. The impact of Zeeman field $B$, Coulomb repulsion $U$
and disorder $\Delta$ is not isolated. The intensity of magnetic field effect
on the antiferromagnetic correlation shall be strongly suppressed by disorder.
Differently, it will be promoted by weak interaction, but when $U$ becomes
larger than $U_{c}=4.5$, the increased interaction will suppress the intensity
of this effect, and here $U_{c}=4.5$ coincides with the critical strength
inducing the metal-Mott insulator transition in clean system. Moreover, at a
fixed magnetic field $B$, strong interaction shall suppress the
antiferromagnetic phase rather than promote it.
