SEMINAR 2023

The Anderson transition, like other continuous phase transitions, exhibits a power law divergence of the correlation length. The exponent appearing in this power law is universal, i.e., its value is determined by only symmetry and dimensionality. This makes it meaningful to estimate its value by simulating simplified models such as Anderson’s model of localisation. The standard technique for analyzing the results of such simulations is finite size scaling (FSS).

I will give an overview of my contribution to FSS studies of the Anderson transition, explaining the basics of the method and more detailed issues such as how to take account of corrections to scaling. I will summarize results for lower and upper critical dimensions, and the dimensionality dependence of the critical exponent in the Wigner-Dyson symmetry classes.

I will report recent results for symmetry class AI in three dimensions. In this universality class, corrections to scaling seem to be well understood. I will contrast this with the case of the critical phenomena of the quantum Hall effect which remains controversial.