Essential spectrum of three-particle discrete operator corresponding to a system of three fermions on a lattice

We consider a family of three-particle discrete Shrödinger operators $H_\mu(K)$, associated to a system of Hamiltonian of three identical particles (fermions) with pairwise two-particles interactions on neighboring junctions on $d$-dimensional lattice $\mathbb{Z}^{d}$. The location and structure of the essential spectrum of the operator $H_\mu(K)$ is described for all three-particles quasi-momentum $K\in \mathbb{T}^d$ and interaction energy $\mu>0$.