The all-orders $\beta$ function is used to study disordered Dirac fermions in two dimensions. The generic strong coupling fixed “points” of anisotropic current-current interactions at large distances are actually isotropic manifolds corresponding to subalgebras of the maximal current algebra at short distances. The argue that IR fixed point theories are generally current algebra cosets. We illustrate this with the simple example of anisotropic $\mathrm{su}\mathrm{}\left(2\right),$ which is the physics of Kosterlitz-Thouless transitions. We propose a phase diagram for the Chalker-Coddington network model which is in the universality class of the integer quantum Hall transition. One phase is in the universality class of dense polymers.

• Received 1 December 2000

DOI:https://doi.org/10.1103/PhysRevB.64.045329