Boundary hopping and the mobility edge in the Anderson model in three dimensions

TL;DR

This paper demonstrates through high-precision simulations that the mobility edge in the 3D Anderson model depends on boundary hopping terms, while the critical exponent remains unaffected, providing insights into the transition's nature.

Contribution

It reveals the dependence of the mobility edge and renormalized localization length on boundary hopping in the 3D Anderson model, highlighting boundary effects on the transition.

Findings

Mobility edge depends on boundary hopping term t.

Critical exponent is independent of boundary hopping.

Renormalized localization length depends on t but not on energy distribution.

Abstract

It is shown, using high-precision numerical simulations, that the mobility edge of the 3d Anderson model depends on the boundary hopping term t in the infinite size limit. The critical exponent is independent of it. The renormalized localization length at the critical point is also found to depend on t but not on the distribution of on-site energies for box and Lorentzian distributions. Implications of results for the description of the transition in terms of a local order-parameter are discussed.