Magnetic phase transition in disordered interacting Dirac fermion systems via the Zeeman field

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.