Infiniteness of the Discrete Spectrum of Two-Particle Discrete Schrödinger Operators

We consider a family of discrete Schrödinger operators where is the two-particle quasi-momentum associated to a system of two particles on the -dimensional lattice . When the pre-image of the two-particle dispersion relation at the right edge of the essential spectrum of is of dimension or , we obtain the necessary and sufficient conditions for the existence of an infinite number of eigenvalues of to the right of the essential spectrum, while in the case , the number of eigenvalues is finite.