Metal-insulator transitions in anisotropic two-dimensional systems - art. no. 085103

Several phenomena related to the critical behavior of noninteracting electr ons in a disordered two-dimensional tight-binding system with a magnetic fi eld are studied. Localization lengths, critical exponents, and density of s tates are computed using transfer-matrix techniques. Scaling functions of i sotropic systems are recovered once the dimension of the system in each dir ection is chosen proportional to the localization length. It is also found that the critical point is independent of the propagation direction, and th at the critical exponents for the localization length for both propagating directions are equal to that of the isotropic system, nu approximate to 7/3 . We also calculate the critical value Lambda (c) of the scaling function f or both the isotropic and the anisotropic system. It is found that Lambda ( iso)(r) = root<(<Lambda>(x)(c)Lambda (y)(c))over bar>. Detailed numerical s tudies of the density of states n(E) for the isotropic system reveal that f or an appreciable amount of disorder, the critical energy is off the band c enter.