The metal--insulator transition in disordered systems: a new approach to the critical behaviour

TL;DR

This paper introduces a new method for studying the Anderson metal-insulator transition that focuses on derivatives with respect to disorder, reducing computational resources and improving efficiency in analyzing critical behavior.

Contribution

The paper proposes an alternative transfer matrix approach that calculates derivatives to better analyze critical behavior in disordered systems, improving efficiency over traditional methods.

Findings

Method allows focus on single energy or disorder value

Potentially reduces computational resources needed

Initial results show advantages and limitations

Abstract

In the most popular approach to the numerical study of the Anderson metal-insulator transition the transfer matrix method is combined with finite-size scaling ideas. This approach requires large computer resources to overcome the statistical fluctuations and to accumulate data for a sufficient range of different values of disorder or energy. In this paper we present an alternative approach in which the basic transfer matrix is extended to calculate the derivative with respect to disorder. By so doing we are able to concentrate on a single value of energy or disorder and, potentially, to calculate the critical behaviour much more efficiently and independently of the assumed range of the critical regime. We present some initial results which illustrate both the advantages and the drawbacks of the method.