Abstract. We study hierarchical network models which have recently been introduced to approximate the Chalker-Coddington model for the integer quantum Hall effect (A.G. Galstyan and M.E. Raikh, PRB 5 (1997) 1422; Arovas et al., PRB 56 (1997) 4751). The hierarchical structure is due to a recursive method starting from a finite elementary cell. The localization-delocalization transition occurring in these models is displayed in the flow of the conductance distribution under increasing system size. We numerically determine this flow, calculate the critical conductance distribution, the critical exponent of the localization length, and the multifractal exponents of critical eigenstates.

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Networks of random quantum scatterers @S-matricesA form paradigmatic models for the propagation of coherent w aves in random media. S-matrix network models cover universal localization-delocalization properties and have some advantages over more traditional Hamiltonian models. In particularD a straightforward implementation of real space renormalization techniques is possible. Starting from a nite elementary cell of the S-matrix networkD hierarchical network models can be constructed by recursion. The localization-delocalization properties are contained in the ow of the forward scattering strength @9conductance9A under increasing system size. With the aid of 9small scale9 n umerics qualitative aspects of the localization-delocalization properties of S-matrix network models can be worked out.

Networks of random quantum scatterers (S‐matrices) form paradigmatic models for the propagation of coherent waves in random media. S‐matrix network models cover universal localization‐delocalization properties and have some advantages over more traditional Hamiltonian models. In particular, a straightforward implementation of real space renormalization techniques is possible. Starting from a finite elementary cell of the S‐matrix network, hierarchical network models can be constructed by recursion. The localization‐delocalization properties are contained in the flow of the forward scattering strength (‘conductance’) under increasing system size. With the aid of ‘small scale’ numerics qualitative aspects of the localization‐delocalization properties of S‐matrix network models can be worked out.

We study hierarchical network models which have recently been introduced to approximate the Chalker-Coddington model for the integer quantum Hall effect (A.G. Galstyan and M.E. Raikh, PRB 5 (1997) 1422; Arovas et al., PRB 56 (1997) 4751). The hierarchical structure is due to a recursive method starting from a finite elementary cell. The localization-delocalization transition Occurring in these models is displayed in the flow of the conductance distribution under increasing system size. We numerically determine this flow, calculate the critical conductance distribution, the critical exponent of the localization length, and the multifractal exponents of critical eigenstates.