Quasi-diffusion in a 3D Supersymmetric Hyperbolic Sigma Model

Margherita Disertori (1) , Tom Spencer (2) , Martin R. Zirnbauer (3)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem
2 School of Mathematics
3 Institut für Theoretische Physik [Köln]

We study a lattice field model which qualitatively reflects the phenomenon of Anderson localization and delocalization for real symmetric band matrices. In this statistical mechanics model, the field takes values in a supermanifold based on the hyperbolic plane. Correlations in this model may be described in terms of a random walk in a highly correlated random environment. We prove that in three or more dimensions the model has a `diffusive' phase at low temperatures. Localization is expected at high temperatures. Our analysis uses estimates on non-uniformly elliptic Green's functions and a family of Ward identities coming from internal supersymmetry.

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

Margherita Disertori, Tom Spencer, Martin R. Zirnbauer. Quasi-diffusion in a 3D Supersymmetric Hyperbolic Sigma Model. Communications in Mathematical Physics, 2010, 300 (2), pp.435-486. ⟨10.1007/s00220-010-1117-5⟩. ⟨hal-00352357⟩