The Anderson-Mott Transition as a Random-Field Problem

TL;DR

This paper models the Anderson-Mott transition as a random-field problem, revealing critical dimensions and exponents similar to the random-field Ising model, with implications for understanding disordered electron systems.

Contribution

It introduces a renormalization group analysis showing the Anderson-Mott transition shares features with classical random-field systems, including critical dimensions and exponents.

Findings

Upper critical dimension is 6 for the model.

Critical behavior is mean-field for dimensions above 6.

Exponents match those of the random-field Ising model below 6.

Abstract

The Anderson-Mott transition of disordered interacting electrons is shown to share many physical and technical features with classical random-field systems. A renormalization group study of an order parameter field theory for the Anderson-Mott transition shows that random-field terms appear at one-loop order. They lead to an upper critical dimension $d_{c}^{+}=6$ for this model. For $d>6$ the critical behavior is mean-field like. For $d<6$ an $\epsilon$-expansion yields exponents that coincide with those for the random-field Ising model. Implications of these results are discussed.