Universality of the critical conductance distribution in various dimensions

Abstract

We study numerically the metal - insulator transition in the Anderson model on various lattices with dimension $2<d\le 4$ (bifractals and Euclidian lattices). The critical exponent $\nu$ and the critical conductance distribution are calculated. We confirm that $\nu$ depends only on the {\it spectral} dimension. The other parameters - critical disorder, critical conductance distribution and conductance cummulants - depend also on lattice topology. Thus only qualitative comparison with theoretical formulae for dimension dependence of the cummulants is possible.

References in corpus (3)

• Reconciling Conductance Fluctuations and the Scaling Theory of Localization
• Symmetry, dimension and the distribution of the conductance at the mobility edge
• The probability distribution of the conductance in anisotropic systems

Cited by in corpus (11)

• Dimensional Dependence of Critical Exponent of the Anderson Transition in the Orthogonal Universality Class
• An attractive critical point from weak antilocalization on fractals
• Possible Anderson transition below two dimensions in disordered systems of noninteracting electrons
• Universal conductance fluctuations in non-integer dimensions
• The phase diagram of the multi-dimensional Anderson localization via analytic determination of Lyapunov exponents
• Character of eigenstates of the 3D disordered Anderson Hamiltonian
• Scattering and transport statistics at criticality
• Metal - Insulator Transition in 3D Quantum Percolation
• Many-body localization on finite generation fractal lattices
• Critical behavior of Anderson transitions in higher dimensional Bogoliubov-de Gennes symmetry classes
• Critical Dynamics of the Anderson Transition on Small-World Graphs