On compact distribution of two-particle Schrödinger operator on a lattice

We consider a system of two arbitrary quantum particles on three-dimensional lattice with certain dispersion functions (they describe a transfer of a particle from one node to another) which with the help of gravity potential interact on nearest neighboring nodes, only. We find a class of potentials such that under perturbation of two-particle operator $h(k)$, which corresponds to a system of two particles with a potential from this class, a discrete operator $h(k)$ is kept.