Kosterlitz-Thouless-Type Metal-Insulator Transition of a 2D Electron Gas in a Random Magnetic Field

We study the localization property of a two-dimensional noninteracting electron gas in the presence of a random magnetic field. The localization length is directly calculated using a transfer matrix technique and finite size scaling analysis. We show strong numerical evidence that the system undergoes a disorder-driven Kosterlitz-Thouless-type metal-insulator transition. We develop a mean field theory which maps the random field system into a two-dimensional $\mathrm{XY}$ model. The vortex and antivortex excitations in the $\mathrm{XY}$ model correspond to two different kinds of magnetic domains in the random field system.