Pulse-noise approach for classical spin systems

TL;DR

The paper introduces a pulse-noise method for simulating classical spin systems, replacing white noise with periodic pulses to improve computational efficiency while maintaining accuracy, especially for small damping constants.

Contribution

It proposes a novel pulse-noise approach that accelerates simulations of classical spins by replacing white noise with regular pulses, enabling larger time steps and faster equilibration.

Findings

Method works well for small damping constants.

Allows larger time steps with high-order integrators.

Achieves equilibration speeds comparable to Monte Carlo.

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 $\Delta t$, 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.