Anderson transition in high dimension: comments to arXiv:2403.01974

TL;DR

This paper critically examines a recent proposal on the Anderson transition in high dimensions, highlighting issues with the use of branching graphs and discussing the validity of the hypothesis presented.

Contribution

It provides a detailed critique of a new approach to the Anderson transition, questioning its assumptions and methodology.

Findings

Identifies flaws in the branching graph approach

Raises doubts about the validity of the proposed hypothesis

Offers alternative perspectives on high-dimensional Anderson transitions

Abstract

In the recent submission arXiv:2403.01974, Altshuler et al suggested a new approach to the Anderson transition in high dimensions. The main idea consists in the use of the branching graphs instead of high-dimensional lattices: it does not look very convincing, but we do not want to stress this point. Since the authors welcome comments, we put forward a lot of objections to their exposition of the general situation. The arising hypothesis is given in the end.