  We construct an integrable lattice model of classical interacting spins in
discrete space-time, representing a discrete-time analogue of the lattice
Landau-Lifshitz ferromagnet with uniaxial anisotropy. As an application we use
this explicit discrete symplectic integration scheme to compute the spin Drude
weight and diffusion constant as functions of anisotropy and chemical
potential. We demonstrate qualitatively different behavior in the easy-axis and
the easy-plane regimes in the non-magnetized sector. Upon approaching the
isotropic point we also find an algebraic divergence of the diffusion constant,
signaling a crossover to spin superdiffusion.
