Spectrum of the two-particle Schrodinger operator on a lattice

We consider the family of two-particle discrete Schrodinger operators H(k) associated with the Hamiltonian of a system of two fermions on a nu-dimensional lattice z(nu) , nu >= 1, where k is an element of T-nu equivalent to (- pi, pi](nu) is a two-particle quasimomentum. We prove that the operator H(k), k is an element of T-nu, k not equal 0, has an eigenvalue to the left of the essential spectrum for any dimension nu = 1, 2, ... if the operator H(0) has a virtual level (nu = 1, 2) or an eigenvalue (nu >= 3) at the bottom of the essential spectrum (of the two-particle continuum).