Localization for a nonlinear sigma model in a strip related to vertex reinforced jump processes
Mathematical Physics
2015-06-16 v1 Statistical Mechanics
math.MP
Probability
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.
Keywords
Cite
@article{arxiv.1308.1293,
title = {Localization for a nonlinear sigma model in a strip related to vertex reinforced jump processes},
author = {Margherita Disertori and Franz Merkl and Silke W. W. Rolles},
journal= {arXiv preprint arXiv:1308.1293},
year = {2015}
}
Comments
45 pages, 3 figures