Reference : Scaling Theory of the Anderson Transition in Random Graphs: Ergodicity and Universality
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Physics
http://hdl.handle.net/2268/209496
Scaling Theory of the Anderson Transition in Random Graphs: Ergodicity and Universality
English
Garcia-Mata, Ignacio []
Giraud, Olivier []
Georgeot, Bertrand []
Martin, John mailto [Université de Liège > Département de physique > Optique quantique >]
Dubertrand, Rémy mailto [Université de Liège > Département de physique > Optique quantique >]
Lemarié, Gabriel []
17-Apr-2017
Physical Review Letters
American Physical Society
118
166801
Yes (verified by ORBi)
International
0031-9007
1079-7114
Ridge
NY
[en] We study the Anderson transition on a generic model of random graphs with a tunable branching parameter 1 < K < 2, through large scale numerical simulations and finite-size scaling analysis. We find that a single transition separates a localized phase from an unusual delocalized phase that is ergodic at large scales but strongly nonergodic at smaller scales. In the critical regime, multifractal wave functions are located on a few branches of the graph. Different scaling laws apply on both sides of the transition: a scaling with the linear size of the system on the localized side, and an unusual volumic scaling on the delocalized side. The critical scalings and exponents are independent of the branching parameter, which strongly supports the universality of our results.
Complex and Entangled Systems from Atoms to Materials - CESAM
CECI
http://hdl.handle.net/2268/209496
10.1103/PhysRevLett.118.166801

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