What is the right form of the probability distribution of the conductance at the mobility edge?

TL;DR

This paper calculates the conductance distribution at the Anderson critical point, revealing differences between 3D and 2D systems, and discusses its universality in disordered systems.

Contribution

It provides the first detailed calculation of the conductance distribution at the Anderson critical point, highlighting differences across dimensions and implications for universality.

Findings

Pc(g) has a dip at small g at the critical point

The distribution differs significantly between 3D and 2D systems

Universality of conductance distributions remains an open question

Abstract

The probability distribution of the conductance Pc(g) at the Anderson critical point is calculated. It is find that Pc(g) has a dip at small g in agreement with epsilon expansion results. The Pc(g) for the 3d system is quite different from the 2d quantum critical point of the integer quantum Hall effect. The universality or not of these distributions is of central importance to the field of disordered systems.