  We study the effects of generic short-ranged interactions on a system of 2D
Dirac fermions subject to a special kind of static disorder, often referred to
as ``chiral.'' The non-interacting system is a member of the disorder class BDI
[M. R. Zirnbauer, J. Math. Phys. 37, 4986 (1996)]. It emerges, for example, as
a low-energy description of a time-reversal invariant tight-binding model of
spinless fermions on a honeycomb lattice, subject to random hopping, and
possessing particle-hole symmetry. It is known that, in the absence of
interactions, this disordered system is special in that it does not localize in
2D, but possesses extended states and a finite conductivity at zero energy, as
well as a strongly divergent low-energy density of states. In the context of
the hopping model, the short-range interactions that we consider are
particle-hole symmetric density-density interactions. Using a perturbative
one-loop renormalization group analysis, we show that the same mechanism
responsible for the divergence of the density of states in the non-interacting
system leads to an instability, in which the interactions are driven strongly
relevant by the disorder. This result should be contrasted with the limit of
clean Dirac fermions in 2D, which is stable against the inclusion of weak
short-ranged interactions. Our work suggests a novel mechanism wherein a clean
system, initially insensitive to interaction effects, can be made unstable to
interactions upon the inclusion of weak static disorder.
