Majorana fermions, whose creation operators are Hermitean, have been proposed and apparently observed in various materials. While only two Majorana fermions are expected to occur in some situations, a whole lattice of them may occur in others, including in a thin film of superconductor on top of a topological insulator in the presence of a magnetic field. A Majorana fermion is then predicted to occur at the core of each superconducting vortex. The ratio of interaction strength to tunneling amplitude for this lattice of Majorana fermions can be tuned to large values by adjusting the chemical potential in the topological insulator. This has motivated us to study the phase diagram of this model, with short range interactions. We find a number of interesting phases and phase transitions, including a critical point which exhibits supersymmetry.