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On the localization transition in three dimensions: Monte-Carlo simulation of a non-linear $σ$-model

Thomas Dupré
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Abstract

We present a combination of analytical and numerical calculations for the critical behavior of a supersymmetric non-linear $σ$-model within the context of the localization transition of a disordered one-electron system. As a result, we obtain a localization length exponent and a set of inverse participation numbers in three dimensions. We find a continuous phase transition with the features of one-parameter scaling and multifractality at the critical point.

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Thomas Dupré. 1995-12-18. On the localization transition in three dimensions: Monte-Carlo simulation of a non-linear $σ$-model. https://doi.org/10.1103/physrevb.54.12763

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