Mean-field limit of the random flux model

TL;DR

This paper analyzes the mean-field limit of a model describing non-interacting electrons on a lattice with random magnetic flux, providing an exact solution for the large orbital limit and comparing it with numerical data.

Contribution

It introduces a mean-field approach to the random flux model by mapping it onto an N-orbital model and derives an exact solution for the N→∞ limit.

Findings

Exact solution for N=∞ limit obtained

Comparison with numerical results shows good agreement

Outline of a 1/N expansion provided

Abstract

The problem of non--interacting electrons on a square lattice subject to a random magnetic flux is mapped onto a one--dimensional model with infinitely many orbitals per site. Linking each orbital with $N(\gg1)$ other orbitals maps the problem onto Wegner's $N$-orbital model in the same limit, while the original problem corresponds to $N=1$. The exact solution for $N=\infty$, the mean--field limit, is discussed and compared with numerical results. An outline of a $1/N$-expansion is given.