Wegner model in high dimension: U(1) symmetry breaking and a non-standard phase of disordered electronic matter, I. One-replica theory

Understand

The Anderson transition between localized and metallic states is traditionally analyzed by assuming a one-parameter scaling hypothesis.

• Although that hypothesis has been confirmed near two dimensions by epsilon = d-2 expansion of the Wegner-Efetov nonlinear sigma model, there exists mounting evidence that the transition in d=3 or higher may have a second branch and that two relevant parameters are needed in order to describe the universal behavior at criticality.
• Doubt of the standard hypothesis also comes from field theory.
• Indeed, increasing the space dimension pushes the Anderson transition towards strong disorder, where a strong-coupling approach very different from the usual weak-coupling analysis of the sigma model is called for.