Critical conductance of the chiral 2d random flux model

TL;DR

This paper investigates the critical conductance behavior of a 2D chiral random flux model at the band center, revealing a scale-invariant conductance point and deriving a critical exponent through numerical analysis.

Contribution

The study provides the first numerical determination of the critical exponent for the 2D chiral flux model's conductance, overcoming finite-size limitations of previous approaches.

Findings

Identifies a scale-invariant critical conductance point.

Derives a critical exponent $ u=0.42\,\pm\,0.05$ for even-width samples.

Shows conductance distribution depends on boundary conditions and lattice size parity.

Abstract

The two-terminal conductance of a random flux model defined on a square lattice is investigated numerically at the band center using a transfer matrix method. Due to the chiral symmetry, there exists a critical point where the ensemble averaged mean conductance is scale independent. We also study the conductance distribution function which depends on the boundary conditions and on the number of lattice sites being even or odd. We derive a critical exponent $\nu=0.42\pm 0.05$ for square samples of even width using one-parameter scaling of the conductance. This result could not be obtained previously from the divergence of the localization length in quasi-one-dimensional systems due to pronounced finite-size effects.