Critical parameters for the disorder-induced metal-insulator transition in FCC and BCC lattices

TL;DR

This study investigates the critical parameters governing the disorder-induced metal-insulator transition in FCC and BCC lattices using transfer-matrix methods, finite-size scaling, and phase diagrams, revealing universal critical exponents and lattice-dependent phase symmetry.

Contribution

It extends previous work on simple cubic lattices to FCC and BCC lattices, providing new phase diagrams and confirming universal critical exponents for these lattice types.

Findings

Critical exponent approximately 1.5-1.6 for both lattices

Phase diagram symmetry varies between BCC and FCC lattices

Critical disorder increases with the number of nearest neighbors

Abstract

We use a transfer-matrix method to study the disorder-induced metal-insulator transition. We take isotropic nearest- neighbor hopping and an onsite potential with uniformly distributed disorder. Following previous work done on the simple cubic lattice, we perform numerical calculations for the body centered cubic and face centered cubic lattices, which are more common in nature. We obtain the localization length from calculated Lyapunov exponents for different system sizes. This data is analyzed using finite-size scaling to find the critical parameters. We create an energy-disorder phase diagram for both lattice types, noting that it is symmetric about the band center for the body centered cubic lattice, but not for the face centered cubic lattice. We find a critical exponent of approximately 1.5-1.6 for both lattice types for transitions occurring either at fixed energy or at fixed disorder, agreeing with results previously obtained for other systems belonging to the same orthogonal universality class. We notice an increase in critical disorder with the number of nearest neighbors, which agrees with intuition.