Communications in Mathematical Physics

, Volume 300, Issue 2, pp 435–486

Quasi-Diffusion in a 3D Supersymmetric Hyperbolic Sigma Model

Open Access

DOI: 10.1007/s00220-010-1117-5

Cite this article as:
Disertori, M., Spencer, T. & Zirnbauer, M.R. Commun. Math. Phys. (2010) 300: 435. doi: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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© The Author(s) 2010

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques Raphaël Salem, UMR CNRS 6085Université de RouenSaint-Étienne-du-RouvrayFrance
  2. 2.Institute for Advanced StudyPrincetonUSA
  3. 3.Institut für Theoretische PhysikUniversität zu KölnKölnGermany

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