Universality of Anderson transition in disordered systems
We review our recent numerical results for the critical regime of Anderson transition for various disordered models.
The universality of the metal-insulator transition in a three-dimensional Anderson model is confirmed by the numerical analysis of the scaling properties of the electronic wave functions. We prove that the critical exponent and the multifractal dimensions are independent on the microscopic definition of the disorder and universal along the critical line which separates the metallic and the insulating regime .
In the integer quantum Hall regime, we calculated the sample averaged longitudinal two-terminal conductance and the respective Kubo-conductivity. In the limit of large system size, both transport quantities are found to be the same within numerical uncertainty in the lowest Landau band, 0.60 +/- 0.02 and 0.58 +/- 0.03, respectively (in units of e^2/h). In the 2nd lowest Landau band, a critical conductance 0.61 +/- 0.03 is obtained which indeed supports the notion of universality. We argue that these values are consistent with the multifractal structure of critical wave functions .
For the symplectic two dimensional Ando model we calculate the critical two-terminal conductance and the spatial fluctuations of critical eigenstates. For square samples, we verify numerically the relation between critical conductivity and the fractal information dimension of the electron wave function. Through a detailed numerical scaling analysis of the two-terminal conductance we also estimate the critical exponent = 2.80 +/- 0.04 .
We study the localization properties and the two-terminal conductance of two-dimensional lattice systems with static random magnetic flux per plaquette and zero mean (systems with chiral symmetry). The influence of boundary conditions and of the oddness of the number of sites in the transverse direction are also studied. Our data are in perfect agreement with previous theoretical predictions. We also find a diverging localization length in the middle of the energy band and determine its critical exponent = 0.35 +/- 0.03. 
 J. Brndiar and P. Markos, Phys. Rev. B 74, 153103 (2006); 77, 115131 (2008)  L. Schweitzer and P. Markos, Phys. Rev. Lett. 95, 256805 (2005)  P. Markos and L. Schweitzer, J. Phys. A 39, 3221 (2006)  P. Markos and L. Schweitzer, Phys. Rev. B 76, 115318 (2007)