Localization and conductance fluctuations in the integer quantum Hall effect: Real-space renormalization-group approach

We consider the network model of the integer quantum Hall effect transition. By generalizing the real-space renormalization-group (RG) procedure for the classical percolation to the case of the quantum percolation, we derive a closed RG equation for the universal distribution of conductance of the quantum Hall sample at the transition. We find the numerical solution of the RG equation and use it to calculate the critical exponent of the localization length and the central moments of the conductance distribution. The results obtained are compared with the results of recent numerical simulations.