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