Localization for a nonlinear sigma model in a strip related to vertex reinforced jump processes

Abstract

We study a lattice sigma model which is expected to reflect Anderson localization and delocalization transition for real symmetric band matrices in 3D, but describes the mixing measure for a vertex reinforced jump process too. For this model we prove exponential localization at any temperature in a strip, and more generally in any quasi-one dimensional graph, with pinning (mass) at only one site. The proof uses a Mermin-Wagner type argument and a transfer operator approach.

45 pages, 3 figures

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• Anderson localization for a supersymmetric sigma model
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Cited by in corpus (4)

• Introduction to a renormalisation group method
• A supersymmetric hierarchical model for weakly disordered $3d$ semimetals
• Strongly vertex-reinforced jump process on a complete graph
• Convergence of vertex-reinforced jump processes to an extension of the supersymmetric hyperbolic nonlinear sigma model