Quantum critical Hall exponents

We investigate a finite size “double scaling” hypothesis using data from an experiment on a quantum Hall system with short range disorder [1], [2], [3]. For Hall bars of width w at temperature T the scaling form is w−μT−κ, where the critical exponent μ≈0.23 we extract from the data is comparable to the multi-fractal exponent α0−2 obtained from the Chalker-Coddington (CC) model [4]. We also use the data to find the approximate location (in the resistivity plane) of seven quantum critical points, all of which closely agree with the predictions derived long ago from the modular symmetry of a toroidal σ-model with m matter fields [5]. The value ν8=2.60513… of the localisation exponent obtained from the m=8 model is in excellent agreement with the best available numerical value νnum=2.607±0.004 derived from the CC-model [6]. Existing experimental data appear to favour the m=9 model, suggesting that the quantum Hall system is not in the same universality class as the CC-model. We discuss the reason this may not be the case, and propose experimental tests to distinguish between the two possibilities.