# Two-Dimensional Electrons in a Strong Magnetic Field with Disorder: Divergence of the Localization Length

Source: [Two-Dimensional Electrons in a Strong Magnetic Field with Disorder: Divergence of the Localization Length](<https://www.sota2.com/research/paper/68fa24342c2a3760193a0953>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T08:56:04.567Z

Authors: K. Ziegler

Published: 1995-05-15T07:45:57.000Z

## Abstract

Electrons on a square lattice with half a flux quantum per plaquette are considered. An effective description for the current loops is given by a two-dimensional Dirac theory with random mass. It is shown that the conductivity and the localization length can be calculated from a product of Dirac Green's functions with the {\\it same} frequency. This implies that the delocalization of electrons in a magnetic field is due to a critical point in a phase with a spontaneously broken discrete symmetry. The estimation of the localization length is performed for a generalized model with $N$ fermion levels using a $1/N$--expansion and the Schwarz inequality. An argument for the existence of two Hall transition points is given in terms of percolation theory.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/9505060>)

[PDF](<https://arxiv.org/pdf/cond-mat/9505060.pdf>)