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We investigate the integer quantum Hall system in a two dimensional latticemodel with spatially correlated disorder by using the efficient method tocalculate the Chern number proposed by Fukui \textit{et al}. Distribution ofcharge density indicates that the extended states at the center of each Landauband have percolating current paths, which are topologically equivalent to theedge states that exist in a system with boundaries. As increasing the strengthof disorder, floating feature is observed in an averaged Hall conductance as afunction of filling factor. Its relation to the observed experiments is alsodiscussed.

Levitation and percolation in quantum Hall systems with correlated disorder