Scaling Properties of 1D Anderson Model with Correlated Diagonal Disorder

TL;DR

This paper investigates how correlations in diagonal disorder affect the scaling properties of the Lyapunov exponent in a 1D Anderson model, revealing an additional parameter influences the single parameter scaling near the band edge.

Contribution

It introduces the impact of correlations on the scaling behavior of the Lyapunov exponent, highlighting an extra parameter that affects the validity of single parameter scaling.

Findings

Correlations modify the scaling properties of the Lyapunov exponent.

An additional parameter governs the validity of single parameter scaling.

The effect is analyzed near the band edge.

Abstract

Statistical and scaling properties of the Lyapunov exponent for a tight-binding model with the diagonal disorder described by a dichotomic process are considered near the band edge. The effect of correlations on scaling properties is discussed. It is shown that correlations lead to an additional parameter governing the validity of single parameter scaling.