  We study excitonic effects in two-dimensional massless Dirac fermions with
Coulomb interactions by solving the ladder approximation to the Bethe-Salpeter
equation. It is found that the general 4-leg vertex has a power law behavior
with the exponent going from real to complex as the coupling constant is
increased. This change of behavior is manifested in the antisymmetric response,
which displays power law behavior at small wavevectors reminiscent of a
critical state, and a change in this power law from real to complex that is
accompanied by poles in the response function for finite size systems,
suggesting a phase transition for strong enough interactions. The
density-density response is also calculated, for which no critical behavior is
found. We demonstrate that exciton correlations enhance the cusp in the
irreducible polarizability at $2k_F$, leading to a strong increase in the
amplitude of Friedel oscillations around a charged impurity.
