  The quantum critical properties of interacting fermions in the presence of
disorder are still not fully understood. While it is well known that for Dirac
fermions, interactions are irrelevant to the non-interacting infinite
randomness fixed point (IRFP), the problem remains largely open in the case of
Majorana fermions which further display a much richer disorder-free phase
diagram. Here, pushing the limits of DMRG simulations, we carefully examine the
ground-state of a Majorana chain with both disorder and interactions. Building
on appropriate boundary conditions and key observables such as entanglement,
energy gap, and correlations, we strikingly find that the non-interacting
Majorana IRFP is very stable against finite interactions, in contrast with
previous claims.
