Quasi-diffusion in a 3D Supersymmetric Hyperbolic Sigma Model

Abstract

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.

55 pages, 6 figures

References in corpus (6)

• Symmetry classes of disordered fermions
• Superbosonization of invariant random matrix ensembles
• Spontaneous symmetry breaking of a hyperbolic sigma model in three dimensions
• Vacuum orbit and spontaneous symmetry breaking in hyperbolic sigma models
• Asymptotic behavior of edge-reinforced random walks
• Structure of the space of ground states in systems with non-amenable symmetries

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