  We introduce a two-ladder lattice model with interacting Majorana fermions
that could be realized on the surfaces of a topological insulator film. We
study this model by a combination of analytical and numerical techniques and
find a phase diagram that features both gapless and gapped phases as well as
interesting phase transitions including a quantum critical point in the
tricritical Ising (TCI) universality class. The latter occurs at an
intermediate coupling strength at a meeting point of a first-order transition
line and an Ising critical line and is known to be described by a
superconformal field theory with central charge $c =\frac{7}{10}$. We discuss
the experimental feasibility of constructing the model and tuning parameters to
the vicinity of the TCI point where signatures of the elusive supersymmetry can
be observed.
