Abstract
Numerical calculations [D. Mattis and S. Rudin, Phys. Rev. Lett. 52, 755 (1984)] indicate the absence of bound states of three identical spin-(1/2) fermions moving on a two-dimensional lattice and interacting with attractive two-body zero-range potentials. Here, we give a proof of this result in the strong-coupling limit, and we also prove that, in the weak-coupling limit, the ground state of six fermions consists of three bound pairs. We discuss the relevance of this result to superconductivity.