Pulse-noise approach for classical spin systems

Abstract

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 ∆t, within which the system evolves conservatively. The method is working well in the typical case of a small dimensionless damping constant λ and allows a considerable speed-up of computations by using high-order numerical integrators with a large time step δt (up to a fraction of the precession period), while keeping δt ∆t to reduce the relative contribution of noise-related operations. In cases when precession can be discarded, δt can be increased up to a fraction of the relaxation time ∝ 1/λ 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.

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Thermal collapse of a skyrmion

“…where T is the temperature. To speed up the numerical integration of the LLL equation, one can replace the continuous white noise by the pulse noise with the period ∆t 43,44 . Noiseless evolution during the interval ∆t between the pulses can be computed by an efficient highorder ODE solver such as fourth-order Runge-Kutta method with the integration step δt ∆t for weak damping.…”

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