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

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

1995-12-18

arxiv.org/abs/cond-mat/9512128v1

Physics

Condensed Matter

14 pages uuencoded postscript-file, 5 figures included

Scientific paper

10.1103/PhysRevB.54.12763

We present a combination of analytical and numerical calculations for the critical behavior of a supersymmetric non-linear $\sigma$-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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