Anderson localization for a supersymmetric sigma model

Margherita Disertori (1) , Tom Spencer (2)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem
2 School of Mathematics

We study a lattice sigma model which is expected to reflect the Anderson localization and delocalization transition for real symmetric band matrices in 3D. In this statistical mechanics model, the field takes values in a supermanifold based on the hyperbolic plane. The existence of a diffusive phase in 3 dimensions was proved for low temperatures. Here we prove localization at high temperatures for any dimension $d\geq 1$. Our analysis uses Ward identities coming from internal supersymmetry.

Mots clés: localization; disorder; supersymmetry

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Margherita Disertori, Tom Spencer. Anderson localization for a supersymmetric sigma model. 2009. ⟨hal-00424690⟩