Critical properties of the metal-insulator transition in anisotropic systems

TL;DR

This study investigates the metal-insulator transition in anisotropic three-dimensional Anderson models, revealing how anisotropy affects critical disorder and confirming the universality of the critical exponent across different anisotropic systems.

Contribution

It provides a detailed numerical analysis of the critical properties of the Anderson transition in anisotropic systems, including critical disorder and exponent estimation.

Findings

Critical disorder decreases with anisotropy following a power law.

Critical exponent estimated as 1.62±0.07, consistent with isotropic models.

Results align with previous studies on multifractal analysis and energy level statistics.

Abstract

We study the three-dimensional Anderson model of localization with anisotropic hopping, i.e., weakly coupled chains and weakly coupled planes. In our extensive numerical study we identify and characterize the metal-insulator transition by means of the transfer-matrix method. The values of the critical disorder $W_c$ obtained are consistent with results of previous studies, including multifractal analysis of the wave functions and energy level statistics. $W_c$ decreases from its isotropic value with a power law as a function of anisotropy. Using high accuracy data for large system sizes we estimate the critical exponent as $\nu=1.62\pm0.07$. This is in agreement with its value in the isotropic case and in other models of the orthogonal universality class.