Geometric integrators for classical spin systems (Q1360401)

Practical, structure preserving methods for integrating classical Heisenberg spin systems are discussed. One of the new integrators, the Lie-Poisson method, is derived based upon a Hamiltonian splitting: it conserves all of the integrals (spin-length and total spin) of the differential equations but the energy. The other integrator is derived based upon a red-black splitting and staggered time stepping. This method is time symmetric and conserves all the available first integrals.The methods are applied to the one- and two-dimensional lattice models and are compared with the commonly used explicit Runge-Kutta, projected Runge-Kutta, and implicit mid point schemes on the basis of accuracy, conservation of invariants and computational expense.