Quasi-diffusion in a 3D Supersymmetric Hyperbolic Sigma Model

Details Quasi-diffusion in a 3D Supersymmetric Hyperbolic Sigma Model Quasi-diffusion in a 3D Supersymmetric Hyperbolic Sigma Model

2009-01-12

arxiv.org/abs/0901.1652v1

Commun.Math.Phys.300:435-486,2010

Physics

Mathematical Physics

55 pages, 6 figures

Scientific paper

10.1007/s00220-010-1117-5

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.

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