Quantum Hall Plateau Transition

The plateau-to-plateau transition between quantum Hall states is a quantum phase transition with critical exponent ν ≈ 2.3. The Landauer conductance G(B,T) obeys one-parameter scaling: G = f((B−B_c)T^{−1/zν}) with z=2.

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σ_xy(B)

Scaling

Critical exponent ν 2.30 Temperature T (log scale) 0.100 Disorder broadening Γ 0.12 Number of temperatures 4

Scaling hypothesis:
σ_xy = n + f(δB / T^{1/zν})

Critical: σ_xy = (n+½)e²/h
ν ≈ 2.3 (Chalker-Coddington)
z = 2 (quantum diffusion)

Slide ν to find best collapse.

Quantum Hall Plateau Transition & Scaling Collapse

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