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We theoretically study the effect of long-ranged inhomogeneities on thecritical properties of the integer quantum Hall transition. For this purpose weemploy the real-space renormalization-group (RG) approach to the network modelof the transition. We start by testing the accuracy of the RG approach in theabsence of inhomogeneities, and infer the correlation length exponent nu=2.39from a broad conductance distribution. We then incorporate macroscopicinhomogeneities into the RG procedure. Inhomogeneities are modeled by a smoothrandom potential with a correlator which falls off with distance as a powerlaw, r^{-alpha}. Similar to the classical percolation, we observe anenhancement of nu with decreasing alpha. Although the attainable system sizesare large, they do not allow one to unambiguously identify a cusp in thenu(alpha) dependence at alpha_c=2/nu, as might be expected from the extendedHarris criterion. We argue that the fundamental obstacle for the numericaldetection of a cusp in the quantum percolation is the implicit randomness inthe Aharonov-Bohm phases of the wave functions. This randomness emulates thepresence of a short-range disorder alongside the smooth potential.Comment: 10 pages including 6 figures, revised version as accepted for  publication in PR

Integer quantum Hall transition in the presence of a long-range-correlated quenched disorder