Tricritical Ising phase transition in two-ladder Majorana fermion lattice

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.