LAUSR

We introduce a deterministic SO(3) invariant dynamics of classical spins on a discrete space–time lattice and prove its complete integrability by explicitly finding a related non-constant (baxterized) solution of the set-theoretic Yang–Baxter equation over the 2-sphere. Equipping the algebraic structure with the corresponding Lax operator we derive an infinite sequence of conserved quantities with local densities. The dynamics depend on a single continuous spectral parameter and reduce to a (lattice) Landau–Lifshitz model in the limit of a small parameter which corresponds to the continuous time limit. Using quasi-exact numerical simulations of deterministic dynamics and Monte Carlo sampling of initial conditions corresponding to a maximum entropy equilibrium state we determine spin-spin spatio-temporal (dynamical) correlation functions with relative accuracy of three orders of magnitude. We demonstrate that in the equilibrium state with a vanishing total magnetization the correlation function precisely follows Kardar–Parisi–Zhang scaling hence the spin transport belongs to the universality class with dynamical exponent $$z=3/2$$ z = 3 / 2 , in accordance to recent related simulations in discrete and continuous time quantum Heisenberg spin 1/2 chains.