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Two-dimensional electron gas in the integer quantum Hall regime isinvestigated numerically by studying the dynamics of an electron hopping on asquare lattice subject to a perpendicular magnetic field and random on-siteenergy with white noise distribution. Focusing on the lowest Landau band weestablish an anti-levitation scenario of the extended states: As either thedisorder strength $W$ increases or the magnetic field strength $B$ decreases,the energies of the extended states move below the Landau energies pertainingto a clean system. Moreover, for strong enough disorder, there is a disorderdependent critical magnetic field $B_c(W)$ below which there are no extendedstates at all. A general phase diagram in the $W-1/B$ plane is suggested with aline separating domains of localized and delocalized states.

Anti-Levitation in the Integer Quantum Hall Systems