Order Parameter Description of the Anderson-Mott Transition

TL;DR

This paper develops an order parameter field theory for the Anderson-Mott transition, revealing its similarities to random-field magnets and calculating critical exponents using renormalization group methods.

Contribution

It introduces a mean-field and renormalization group framework for the AMT, showing its upper critical dimension and connection to random-field Ising model exponents.

Findings

Mean-field critical exponents are exact above the upper critical dimension.

An upper critical dimension of 6 is established for the AMT.

Critical exponents below 6 dimensions match those of the random-field Ising model.

Abstract

An order parameter description of the Anderson-Mott transition (AMT) is given. We first derive an order parameter field theory for the AMT, and then present a mean-field solution. It is shown that the mean-field critical exponents are exact above the upper critical dimension. Renormalization group methods are then used to show that a random-field like term is generated under renormalization. This leads to similarities between the AMT and random-field magnets, and to an upper critical dimension $d_{c}^{+}=6$ for the AMT. For $d<6$, an $\epsilon = 6-d$ expansion is used to calculate the critical exponents. To first order in $\epsilon$ they are found to coincide with the exponents for the random-field Ising model. We then discuss a general scaling theory for the AMT. Some well established scaling relations, such as Wegner's scaling law, are found to be modified due to random-field effects. New experiments are proposed to test for random-field aspects of the AMT.