Critical properties of the metal-insulator transition in anisotropic systems

摘要

We study the three-dimensional Anderson model of localization withanisotropic hopping, i.e., weakly coupled chains and weakly coupled planes. Inour extensive numerical study we identify and characterize the metal-insulatortransition by means of the transfer-matrix method. The values of the criticaldisorder $W_c$ obtained are consistent with results of previous studies,including multifractal analysis of the wave functions and energy levelstatistics. $W_c$ decreases from its isotropic value with a power law as afunction of anisotropy. Using high accuracy data for large system sizes weestimate the critical exponent as $\nu=1.62\pm0.07$. This is in agreement withits value in the isotropic case and in other models of the orthogonaluniversality class.