Energy balance and energy correction in dynamics of classical spin systems

TL;DR

This paper introduces an energy correction method for classical spin system simulations, improving energy conservation in long-term computations and making standard integrators more competitive with symplectic methods.

Contribution

It proposes a novel energy correction technique that enhances the accuracy of mainstream integrators for classical spin dynamics, especially with single-site interactions.

Findings

The method improves energy conservation in long simulations.

It enables mainstream integrators to compete with symplectic ones.

A formula for dynamical spin temperature with anisotropy is derived.

Abstract

Energy-correction method is proposed as an addition to mainstream integrators for equations of motion of systems of classical spins. This solves the problem of non-conservation of energy in long computations and makes mainstream integrators competitive with symplectic integrators for spin systems that for different-site interactions conserve the energy explicitly. The proposed method is promising for spin systems with single-site interactions for which symplectic integrators do not conserve energy and thus have no edge against mainstream integrators. From the energy balance in the spin system with a phenomenological damping and Langevin fields, a formula for the dynamical spin temperature in the presence of single-site anisotropy is obtained.