The essential spectrum of the three-particle discrete operator corresponding to a system of three fermions on a lattice

We consider a family of three-particle discrete Shrödinger operators H _μ (K). These operators are associated with the Hamiltonian for a system of three identical particles (fermions) with pairwise two-particle interactions on neighboring junctions of the d-dimensional lattice Z ^d . We describe the location and the structure of the essential spectrum of the operator H _μ (K) for all values of the three-particle quasi-momentum K ∈ T ^d and the interaction energy μ > 0.