Order Parameter Description of the Anderson-Mott Transition

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.

28pp., REVTeX, no figures

References in corpus (2)

• A Landau Theory for the Metal-Insulator Transition
• The Anderson-Mott Transition as a Random-Field Problem

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