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

Abstract

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.

14 pages uuencoded postscript-file, 5 figures included

References in corpus (6)

• Mutifractal Analysis of Broadly Distributed Observables at Criticality
• Statistics of pre-localized states in disordered conductors
• Relation between Energy Level Statistics and Phase Transition and its Application to the Anderson Model
• Multifractality: generic property of eigenstates of 2D disordered metals.
• Scaling of Level Statistics at the Disorder-Induced Metal-Insulator Transition
• Distribution of local density of states in disordered metallic samples: logarithmically normal asymptotics

Cited by in corpus (3)

• Quasi-diffusion in a 3D Supersymmetric Hyperbolic Sigma Model
• Anderson localization for a supersymmetric sigma model
• Phase Transition in a Model with Non-Compact Symmetry on Bethe Lattice and the Replica Limit