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A Landau Theory for the Metal-Insulator Transition

T. R. Kirkpatrick·D. Belitz
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Abstract

The nonlinear $σ$-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 $ϕ^4$-theory with the single-particle density of states as the order parameter. All static exponents have their mean-field values, and the dynamical exponent $z=3$. $\partial n/ \partial μ$ 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 $2+ε$ expansion.

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T. R. Kirkpatrick, D. Belitz. 1994-02-15. A Landau Theory for the Metal-Insulator Transition. https://doi.org/10.1103/physrevlett.73.862

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