  The search for departures from standard hydrodynamics in many-body systems
has yielded a number of promising leads, especially in low dimension. Here we
study one of the simplest classical interacting lattice models, the
nearest-neighbour Heisenberg chain, with temperature as tuning parameter. Our
numerics expose strikingly different spin dynamics between the antiferromagnet,
where it is largely diffusive, and the ferromagnet, where we observe strong
evidence either of spin super-diffusion or an extremely slow crossover to
diffusion. This difference also governs the equilibration after a quench, and,
remarkably, is apparent even at very high temperatures.
