Upper critical dimension in the scaling theory of localization

TL;DR

This paper proposes a two-parameter scaling theory for localization phenomena, highlighting the importance of off-diagonal disorder and explaining the concept of an upper critical dimension within this framework.

Contribution

It introduces a two-parameter scaling approach that extends the traditional theory by incorporating off-diagonal disorder effects.

Findings

The Thouless number g(L) alone is insufficient for scale transformations.

A second parameter related to off-diagonal disorder is necessary.

The theory explains the upper critical dimension in localization phenomena.

Abstract

It is argued that the Thouless number g(L) is not the only parameter relevant in scale transformations, and that the second parameter connected with off-diagonal disorder should be introduced. A two-parameter scaling theory is suggested that explains a phenomenon of the upper critical dimension from the viewpoint of scaling ideas.