Abstract
The description of all integrable deformations of the Heisenberg model, which are linear in terms of the deformation constants, is given in the present paper. Besides the well-known Landau-Lifshitz integrable model with a biaxial anisotropy there exists one isotropic integrable deformation, one anisotropic deformation with a biaxial anisotropy, and one integrable deformation with a uniaxial anisotropy.
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