Analytical realization of finite-size scaling for Anderson localization. Does the band of critical states exist for d>2?

TL;DR

This paper presents an analytical approach to finite-size scaling in Anderson localization, suggesting the existence of a band of critical states for dimensions greater than two, supported by numerical evidence.

Contribution

It introduces an analytical realization of finite-size scaling based on auxiliary quasi-1D systems, proposing a new perspective on the Anderson transition.

Findings

The Anderson transition point is split into a band of critical states.

Numerical evidence supports the existence of a critical state band.

Reinterpretation of raw numerical data may be necessary for conventional understanding.

Abstract

An analytical realization is suggested for the finite-size scaling algorithm based on the consideration of auxiliary quasi-1D systems. Comparison of the obtained analytical results with the results of numerical calculations indicates that the Anderson transition point is splitted into the band of critical states. This conclusion is supported by direct numerical evidence (Edwards and Thouless, 1972; Last and Thouless, 1974; Schreiber, 1985; 1990). The possibility of restoring the conventional picture still exists but requires a radical reinterpretetion of the raw numerical data.