Tommaso Rizzo

(Institute of Complex Systems Rome (ISC-CNR) and Dipartimento di Fisica Università Sapienza)

 

Abstract:
I discuss Anderson localization on lattices that are tree-like except for the presence of one single loop of varying length L. The resulting analysis allows to compute corrections to the Bethe lattice solution on i) Random-Regular-Graph (RRG) of finite size N and ii) euclidean lattices in finite dimension. In the first case the prefactor of the 1/N corrections to the average values of the typical density of states diverges exponentially approaching the critical point. This explains the puzzling observation that the numerical simulations on finite RRGs deviate spectacularly from the expected asymptotic behavior. In the second case the results, combined with the M -layer expansion, predict that corrections destroy the exotic critical behavior of the Bethe lattice solution in any finite dimension. This strengthens the suggestion that the upper critical dimension of Anderson localization is infinity and opens the way to the computation of non-mean-field critical exponents by resumming the series of diverging diagrams through the same recipes of the field-theoretical perturbative expansion.

Work done in Collaboration with M. Baroni, G. Garcia Lorenzana and M. Tarzia
 

Zoom registration link:
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