Validity of geometrically disordered mixed classical–quantum network models for the integer QHE

Determine whether geometrically disordered network models that mix fully open or fully closed classical scattering nodes with Chalker–Coddington quantum nodes genuinely capture the physics of the integer quantum Hall effect plateau–to–plateau transitions, by establishing whether their critical behavior and universality class coincide with those of the Chalker–Coddington model.

Background

Experimental measurements of the localization length critical exponent in the integer quantum Hall effect typically yield values around 2.38, while recent high-precision numerical studies of the Chalker–Coddington network model report higher values near 2.59. To reconcile this discrepancy, several works proposed network models that mix classical open/closed nodes with quantum Chalker–Coddington nodes (“geometric disorder”), claiming such mixing can reduce the exponent towards experimental values.

Despite this motivation, the authors note uncertainty about whether these mixed classical–quantum models truly represent the QHE plateau transitions. Their own real-space renormalization study of the mixed model finds sensitivity to the renormalization unit geometry and critical exponents that do not correspond to known universality classes, underscoring the unresolved status of the model’s validity for the QHE.