Reentrant behaviour and universality in the Anderson transition

The three-dimensional Anderson model with a rectangular distribution of site disorder displays two distinct localization-delocalization transitions, against varying disorder intensity, for a relatively narrow range of Fermi energies. Such transitions are studied through the calculation of localization lengths of quasi-- one-dimensional systems by transfer-matrix methods, and their analysis by finite-size scaling techniques. For the transition at higher disorder we find the localization-length exponent $ν=1.60(5)$ and the limiting scaled localization-length amplitude $Λ_0=0.57(1)$, strongly suggesting universality with the transition at the band centre, for which currently accepted values are $ν=1.57(2)$ and $Λ_0=0.576(2)$. For the lower (reentrant) transition, we estimate $ν=1.55(15)$ and $Λ_0=0.55(5)$, still compatible with universality but much less precise, partly owing to significant finite-size corrections.

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