Configuration and Self-averaging in disordered systems

TL;DR

This paper compares two methodologies for configuration averaging in disordered systems, applying them to disordered graphene to explore the concept of spatial ergodicity and why single samples often reflect averaged properties.

Contribution

It introduces and compares the Recursion method and Augmented space formalism for configuration averaging, providing insights into spatial ergodicity in disordered systems.

Findings

Both methods yield similar results within error margins for disordered graphene.

The study reexamines the concept of spatial ergodicity in disordered systems.

The methodologies are effective for understanding configuration averaging in disordered materials.

Abstract

The main aim of this work is to present two different methodologies for configuration averaging in disordered systems. The Recursion method is suitable for the calculation of spatial or self-averaging, while the Augmented space formalism averages over different possible configurations of the system. We have applied these techniques to a simple example and compared their results. Based on these, we have reexamined the concept of spatial ergodicity in disordered systems. The specific aspect, we have focused on, is the question "Why does an experimentalist often obtain the averaged result on a single sample ?" We have found that in our example of disordered graphene, the two lead to the same result within the error limits of the two methods.