“…Unfortunately, symplectic integrators for spin systems have only rarely been considered in the literature, see [6,7,8]. The method of the independent time evolution of sublattices, proposed in [6,9,10], is volume-preserving but not symplectic, see 2.2.1 and [6]. Inspired by [10], we suggest to construct symplectic integrators based on a splitting of the spin Hamiltonian into two completely integrable Hamiltonians belonging to a special kind of systems [11,12].…”