The Large Connectivity Limit of the Anderson Model on Tree Graphs
arXiv:1303.4908 · doi:10.1063/1.4894055
Abstract
We consider the Anderson localization problem on the infinite regular tree. Within the localized phase, we derive a rigorous lower bound on the free energy function recently introduced by Aizenman and Warzel. Using a finite volume regularization, we also derive an upper bound on this free energy function. This yields upper and lower bounds on the critical disorder such that all states at a given energy become localized. These bounds are particularly useful in the large connectivity limit where they match, confirming the early predictions of Abou-Chacra, Anderson and Thouless.
20 pages, 3 figures (published version)
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- Critical behavior of the Anderson model on the Bethe lattice via a large-deviation approach
- Anderson Localization on the Bethe Lattice using Cages and the Wegner Flow
- Out of equilibrium Phase Diagram of the Quantum Random Energy Model
- On the Wegner orbital model
- Tracy-Widom at high temperature
- Anderson Localization on Husimi Trees and its implications for Many-Body localization