M. Bauer et O. Golinelli, Exactly solvable model with two conductor-insulator transitions driven by impurities, PHYS REV L, 86(12), 2001, pp. 2621-2624
We present an exact analysis of two conductor-insulator transitions in the
random graph model where low connectivity means high impurity concentration
. The adjacency matrix of the random graph is used as a hopping Hamiltonian
. We compute the height of the delta peak at zero energy in its spectrum ex
actly and describe analytically the structure and contribution of localized
eigenvectors. The system is a conductor for average connectivities between
1.421 529... and 3.154 985... but an insulator in the other regimes. We ex
plain the spectral singularity at average connectivity e = 2.718 281... and
relate it to other enumerative problems in random graph theory.