The spectral statistics of a Cayley tree are numerically studied. The statistics are nonuniversal due to the high ratio of boundary sites. Once the boundary sites are connected to each other in a way that preserves the local structure of the tree, the universal statistics of the spectra is recovered. A clear localization transition is observed as function of on-site disorder strength, with a critical disorder Wc = 11.44±0.08 and critical index ν = 0.51±0.05. The value of ν fits nicely to its mean-field value, while the value of Wc is puzzling.
|Journal||Physical Review B - Condensed Matter and Materials Physics|
|State||Published - 17 Nov 2003|