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 generate under renormalization. This leads to similarities between the AMT and random-field magnets, and to an upper critical dimensiond +c =6 for the AMT. Ford<6, and ε=6−d expansion is used to calculate the critical exponents. To first order in ε 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.
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References
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