DIRAC FERMIONS WITH DISORDER IN 2 DIMENSIONS - EXACT RESULTS

Dirac fermions on a two-dimensional lattice with disorder are consider ed. The Dirac mass, which controls the gap between the two bands of th e fermions, is subject to random fluctuations. Another type of disorde r is discussed presented by a random vector potential. It is shown tha t the imaginary part of the one-particle Green's function can be writt en as the imaginary part of another Green's function, which has only p oles on the lower half plane. Therefore, it is possible to perform a C auchy integration for a Lorentzian distribution in analogy with the Ll oyd model. The results are compared with calculations performed in the continuum limit based on renormalization group and bosonization metho ds.