Event-chain Monte Carlo for classical continuous spin models

TL;DR

This paper demonstrates that the event-chain Monte Carlo algorithm significantly improves sampling efficiency for classical continuum spin models, especially in complex systems like 3D XY spin glasses, compared to traditional methods.

Contribution

It introduces the application of event-chain Monte Carlo to lattice spin models and clarifies the conditions for its effectiveness.

Findings

Outperforms local Monte Carlo by two orders of magnitude in 2D XY model

Far superior to other algorithms in 3D XY spin glass at low temperature

Remains slower than Wolff cluster algorithm in 2D XY model

Abstract

We apply the event-chain Monte Carlo algorithm to classical continuum spin models on a lattice and clarify the condition for its validity. In the two-dimensional XY model, it outperforms the local Monte Carlo algorithm by two orders of magnitude, although it remains slower than the Wolff cluster algorithm. In the three-dimensional XY spin glass at low temperature, the event-chain algorithm is far superior to the other algorithms.