Critical behavior of structurally disordered quantum Hall network models from an alternative scaling variable

The nature of the quantum Hall plateau transition is a decades-old puzzle. The current consensus is that the Chalker Coddington network model captures the transition physics. Numerous works have used Lyapunov exponent finite-size scaling to calculate the localization length critical exponent ν ~ 2.6. However, calculations with the same methods on structurally disordered networks give a slightly different yet incompatible result, ν ~ 2.38, suggesting that structural disorder may be a relevant perturbation at the underlying fixed point. To further probe and understand this surprising finding, we study structurally disordered networks with an alternative scaling variable. This variable is based on the networks’ scattering matrices and does not require the quasi-1d geometry of conventional methods. We study networks an order of magnitude larger than the current literature standard to confirm the relevance of structural disorder and we also address the idea of marginal scaling at the critical point. Finally, we examine how these results are compatible with the Harris criterion.