Universität zu Köln

Disertori, M., Spencer, T. and Zirnbauer, M. R. (2010). Quasi-Diffusion in a 3D Supersymmetric Hyperbolic Sigma Model. Commun. Math. Phys., 300 (2). S. 435 - 487. NEW YORK: SPRINGER. ISSN 1432-0916

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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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Disertori, M. UNSPECIFIED UNSPECIFIED UNSPECIFIED Spencer, T. UNSPECIFIED UNSPECIFIED UNSPECIFIED Zirnbauer, M. R. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-491288
DOI:	10.1007/s00220-010-1117-5
Journal or Publication Title:	Commun. Math. Phys.
Volume:	300
Number:	2
Page Range:	S. 435 - 487
Date:	2010
Publisher:	SPRINGER
Place of Publication:	NEW YORK
ISSN:	1432-0916
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language SPONTANEOUS SYMMETRY-BREAKING; LOCALIZATION; DIMENSIONS; STATES Multiple languages Physics, Mathematical Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/49128