The localization transition on the Bethe lattice

H. Kunz , B. Souillard

We present exact results concerning the localization transition on the Bethe lattice. In a certain number of situations, we prove the existence of a transition from extended to localized regime when varying the energy or the disorder. The density of states is analytic at the mobility edges and the exponent ν governing the divergence of the localization length is found equal to 1.

Mots clés: lattice theory and statistics; localised electron states; critical exponent; extended regime; metal insulator transition; localization transition; Bethe lattice; disorder; density of states; mobility edges

Domaines: Articles anciens

H. Kunz, B. Souillard. The localization transition on the Bethe lattice. Journal de Physique Lettres, 1983, 44 (11), pp.411-414. ⟨10.1051/jphyslet:019830044011041100⟩. ⟨jpa-00232210⟩