  The appearence of long-range correlations near the Dirac point of a
Dirac-like spinor model with random vector potential is studied. These
correlations originate from a spontaneously broken symmetry and their
corresponding Goldstone modes. Using a strong-disorder expansion, correlation
functions and matrix elements are analyzed and compared with results from a
weak-disorder expansion. The local density of states correlation and the
overlap between states above and below the Dirac point are characterized by a
long-range behavior. The correlation range decreases with the distance from the
Dirac point. Transport is diffusive and the diffusion coefficient is
proportional to the one-particle scattering time for any strength of disorder.
A consequence of the special properties of particle-hole scattering is a
constant microwave conductivity for weak as well as for strong disorder,
describing a deviation from conventional Drude-like transport. Some properties
of the model can be linked to a kind of Kondo scale, which is generated by
disorder. Finally, the properties of the wave functions at the Dirac point are
characterized by their participation ratios, indicating a critical state at the
Dirac point.
