A Landau Theory for the Metal-Insulator Transition

Abstract

The nonlinear $\sigma$-model for disordered interacting electrons is studied in spatial dimensions $d>4$. The critical behavior at the metal-insulator transition is determined exactly, and found to be that of a standard Landau-Ginzburg-Wilson $\phi^4$-theory with the single-particle density of states as the order parameter. All static exponents have their mean-field values, and the dynamical exponent $z=3$. $\partial n/ \partial \mu$ is critical with an exponent of $1/2$, and the electrical conductivity vanishes with an exponent $s=1$. The transition is qualitatively different from the one found in the same model in a $2+\epsilon$ expansion.