Abstract
In this paper we propose a new S-matrix approach to numerical simulations of network models and apply it to random networks that we proposed in a previous work 10.1103/PhysRevB.95.125414. Random networks are modifications of the Chalker-Coddington (CC) model for the integer quantum Hall transition that more faithfully capture the physics of electrons moving in a strong magnetic field and a smooth disorder potential. The new method has considerable advantages compared to the transfer matrix approach, and gives the value ν ≈ 2.4 for the critical exponent of the localization length in a random network. This finding confirms our previous result and is surprisingly close to the experimental value ν_exp ≈ 2.38 observed at the integer quantum Hall transition but substantially different from the CC value νCC ≈ 2.6.