Pulse-noise approach for classical spin systems
  For systems of classical spins interacting with the bath via damping and thermal noise, the approach is suggested to replace the white noise by a pulse noise acting at regular time intervals $\Delta t$, within which the system evolves conservatively. The method is working well in the typical case of a small dimensionless damping constant $\lambda$ and allows a considerable speed-up of computations by using high-order numerical integrators with a large time step $\delta t$ (up to a fraction of the precession period), while keeping $\delta t\ll\Delta t$ to reduce the relative contribution of noise-related operations. In cases when precession can be discarded, $\delta t$ can be increased up to a fraction of the relaxation time $\propto1/\lambda$ that leads to a further speed-up. This makes equilibration speed comparable with that of Metropolis Monte Carlo. The pulse-noise approach is tested on single-spin and multi-spin models. 
D. A. Garanin
cond-mat.stat-mech physics.comp-ph