Phase Diagram for Anderson Disorder: beyond Single-Parameter Scaling

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dc.creatorGoldenfeld, Nigel
dc.creatorHaydock, Roger
dc.date2005-09-21
dc.date2005-11-30
dc.date.accessioned2026-07-07T06:41:50Z
dc.date.available2026-07-07T06:41:50Z
dc.descriptionThe Anderson model for independent electrons in a disordered potential is transformed analytically and exactly to a basis of random extended states leading to a variant of augmented space. In addition to the widely-accepted phase diagrams in all physical dimensions, a plethora of additional, weaker Anderson transitions are found, characterized by the long-distance behavior of states. Critical disorders are found for Anderson transitions at which the asymptotically dominant sector of augmented space changes for all states at the same disorder. At fixed disorder, critical energies are also found at which the localization properties of states are singular. Under the approximation of single-parameter scaling, this phase diagram reduces to the widely-accepted one in 1, 2 and 3 dimensions. In two dimensions, in addition to the Anderson transition at infinitesimal disorder, there is a transition between two localized states, characterized by a change in the nature of wave function decay.
dc.description51 pages including 4 figures, revised 30 November 2005
dc.identifierhttps://arxiv.org/abs/cond-mat/0509550
dc.identifierhttp://arxiv.org/abs/cond-mat/0509550
dc.identifierPhysical Review B, vol. 73, 045118 (2006) 10 pages
dc.identifierdoi:10.1103/PhysRevB.73.045118
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/101813
dc.subjectStrongly Correlated Electrons
dc.subjectDisordered Systems and Neural Networks
dc.titlePhase Diagram for Anderson Disorder: beyond Single-Parameter Scaling
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