Exactly solvable model of fermions with disorder

Abstract

Nonperturbative results are obtained for multipoint correlation functions of the model of (2+1)-dimensional relativistic fermions in a random non-Abelian gauge potential. At zero frequencies the model is a critical theory with power law behavior of correlation functions. The average distance between the energy levels scales as ${\mathit{L}}^{\mathrm{-}2+1/\mathit{N}2}$, where L is the system’s size and N is the number of components of the fermionic field. We calculate the diffusion propagator and show that the dc conductivity for this model is finite.