J. Phys. I France
Volume 4, Numéro 4, April 1994
Page(s) 551 - 564
DOI: 10.1051/jp1:1994159
J. Phys. I France 4 (1994) 551-564

Metal-insulator transition in two-dimensional Ando model

P. Markos

Institute of Physics, Slovak Academy of Sciences Dtibravskâ cesta 9, 842 28 Bratislava, Slovakia

(Received 6 September 1993, received in final form 10 December 1993, accepted 20 December 1993)

The transport properties of the Ando model on square lattice are studied numerically for box distribution of the diagonal disorder. The statistical properties of the Lyapunov exponents and of the conductance are discussed. It is shown that the statistics of the Lyapunov exponents agrees with the random matrix theory not only in the metallic regime, but even at the critical point. That confirms the applicability of the random matrix theory to the description of the metal-insulator transition. The limiting distribution of the conductance at the critical point of the metal-insulator transition is presented and its foret is discussed on the base of the statistics of the Lyapunov exponents. Fluctuations of the conductance in the metallic and of the logarithm of the conductance in the insulating regimes indicate that the theory of the metal-insulator transition is one-parametric.

© Les Editions de Physique 1994