Critical properties of the metal-insulator transition in anisotropic systems

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 Wc obtained are consistent with results of previous studies, including multifractal analysis of the wave functions and energy level statistics. Wc 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 ν = 1.62 ± 0.07. This is in agreement with its value in the isotropic case and in other models of the orthogonal universality class. PACS. 71.30.+h Metal-insulator transitions and other electronic transitions – 72.15.Rn Localization effects (Anderson or weak localization) – 73.20.Dx Electron states in low-dimensional structures (superlattices, quantum well structures and multilayers)