Divergences of the localization lengths in the two- dimensional, off-diagonal Anderson model on bipartite lattices

摘要

We investigate the scaling properties of the two-dimensional (2D) Andersonmodel of localization with purely off-diagonal disorder (random hopping). Usingthe transfer-matrix method and finite-size scaling we compute the infinite-sizelocalization lengths for bipartite square and hexagonal 2D lattices,non-bipartite triangular lattices and different distribution functions for thehopping elements. We show that for small energies the localization lengths inthe bipartite case diverge with a power-law behavior. The correspondingexponents are in the range $0.2 - 0.6$ and seem to depend on the type and thestrength of disorder.