Data for Real-space renormalisation approach to the Chalker-Coddington model revisited : improved statistics

Previous such studies found $\nu\sim 2.39$ which falls considerably short of the current best estimates by transfer matrix ($\nu=2.593 \substack{+0.005\\-0.006}$) and exact-diagonalisation studies ($\nu=2.58(3)$).

By increasing the amount of data $500$ fold we can now measure closer to the critical point and find an improved estimate $\nu=2.51\substack{+0.11\\-0.11}$. This deviates only $\sim 3\%$ from the previous two values and is already better than the $\sim 7\%$ accuracy of the classical small-cell renormalisation approach from which our method is adapted. We also study a previously proposed mixing of the Chalker-Coddington model with a classical scattering model which is meant to provide a route to understanding why experimental estimates give a lower $\nu\sim 2.3$.