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We consider a two-magnon system in the isotropic Heisenberg ferromagnet model with impurity on a ν-dimensional lattice Z with nearest-neighbor interaction and study the essential and discrete spectra of this system. We first describe the model with a finite number of spins (see [1]). Let Λ be a finite subset in Z . We assign a copy of the space C to each point t ∈ Z and let Ct denote it. We consider the Hilbert space HΛ = ⊗ t∈Λ C 2 t . Let σ, σ , and σ be the Pauli matrices, i.e., σ = ( 0 1 1 0 ) , σ = ( 0 −i i 0 ) , and σ = ( 1 0 0 −1 ) . We set σ± ≡ (σ ± iσ)/2. For each t ∈ Λ, we let σ t , σ y t , σ z t , and σ ± t denote the operators in HΛ respectively acting on the tth component of the tensor product as σ, σ, σ , and σ± and acting on the other components as the unit matrix. The Heisenberg Hamiltonian is defined as

Спектр оператора энергии двухмагнонных систем в изотропной примесной ферромагнитной модели Гейзенберга