Electronic density of states on a randomly dilute Cayley tree

The density of states on a randomly dilute Cayley tree (bonds are present with probability p) has been obtained both numerically and analytically. The numerical procedure involves an average over randomly generated clusters of the dilute Cayley tree, whereas the analytical procedures define an effective medium through a self-consistency equation. One of them extends the coherent potential approximation to include the effect of nondiagonal disorder in disconnected lattices. This approximation reproduce very well the authors' simulation results in the whole range of dilution (0<p<1).