  Quasi-one-dimensional spin-Peierls and spin-ladder systems are characterized
by a gap in the spin-excitation spectrum, which can be modeled at low energies
by that of Dirac fermions with a mass. In the presence of disorder these
systems can still be described by a Dirac fermion model, but with a random
mass. Some peculiar properties, like the Dyson singularity in the density of
states, are well known and attributed to creation of low-energy states due to
the disorder. We take one step further and study single-particle correlations
by means of Berezinskii's diagram technique. We find that, at low energy
$\epsilon$, the single-particle Green function decays in real space like
$G(x,\epsilon) \propto (1/x)^{3/2}$. It follows that at these energies the
correlations in the disordered system are strong -- even stronger than in the
pure system without the gap. Additionally, we study the effects of boundaries
on the local density of states. We find that the latter is logarithmically (in
the energy) enhanced close to the boundary. This enhancement decays into the
bulk as $1/\sqrt{x}$ and the density of states saturates to its bulk value on
the scale $L_\epsilon \propto \ln^2 (1/\epsilon)$. This scale is different from
the Thouless localization length $\lambda_\epsilon\propto\ln (1/\epsilon)$. We
also discuss some implications of these results for the spin systems and their
relation to the investigations based on real-space renormalization group
approach.
