The integer quantum Hall transition: an $S$-matrix approach to random networks

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 $\nu \approx 2.4$ 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 $\nu_{\text{exp}} \approx 2.38$ observed at the integer quantum Hall transition but substantially different from the CC value $\nu_\text{CC} \approx 2.6$.