Exact shape of the lowest Landau level in a spin-1/2 system with   uncorrelated disorders
  Using the path-integral approach developed by Br\'ezin et al. [ Nucl.Phys.B235, 24 (1984) ], we obtain an analytical expression for the density of states of a spin-1/2 disordered two-dimensional electron gas in a strong, perpendicular magnetic field. The density of states of this system illustrates the interplay between the Zeeman splitting of Landau levels and the disorder-induced broadening. We find that the broadening and the band splitting of the Landau bands are enhanced due to the level repulsion from the mixing of two spin orientations caused by the random scatterings. The comparison between the spin-1/2 model and the double-layer system is also discussed. 
Ming-Hsien Tu and Min-Fong Yang