Three-body bound states on a lattice

The theory of three-body bound states for particles moving on a lattice and interacting with attractive two-body pointlike potentials is presented. The applications are to bosons, fermions (no three-body bound states are found), and magnons. When a three-body bound state forms in three dimensions, it does so discontinuously. Thus there is a maximum size for the three-body bound state, of approximately two lattice constants. Some of the various analyses are relevant to magnetism and superconductivity.