  We study a tight-binding model of interacting Majorana (Hermitian) modes on a
square lattice. The model may have an experimental realization in a
superconducting-film--topological-insulator heterostructure in a magnetic
field. We find a rich phase diagram, as a function of interaction strength,
including a superfluid phase with spontaneous breaking of an emergent $U(1)$
symmetry, separated by a supersymmetric transition from a gapless normal phase.
