ORDER-PARAMETER DESCRIPTION OF THE ANDERSON-MOTT TRANSITION

An order parameter description of the Anderson-Molt transition (AMT) i s 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-fiel d critical exponents are exact above the upper critical dimension. Ren ormalization group methods are then used to show that a random-field l ike term is generated under renormalization. This leads to similaritie s between the AMT and random-field magnets, and to an upper critical d imension d(c)(+) = 6 for the AMT. For d < 6, an epsilon = 6 - d expans ion is used to calculate the critical exponents. To first order in eps ilon they are found to coincide with the exponents for the random-fiel d Ising model. We then discuss a general scaling theory for the AMT. S ome well established scaling relations such as Wegner's scaling law, a re found to be modified due to random-field effects. New experiments a re proposed to test for random-field aspects of the AMT.