Testing the event-chain algorithm in asymptotically free models

TL;DR

This paper evaluates the event-chain algorithm on toy lattice QCD models, demonstrating its stability and effectiveness in significantly reducing critical slowing down across various models.

Contribution

The paper provides a formal proof of the algorithm's stability and demonstrates its performance in eliminating critical slowing down in multiple lattice models.

Findings

Critical slowing down is essentially eliminated in tested models.

The event-chain algorithm is stable for lattice QCD toy models.

Performance improvements are observed in Gaussian and non-linear sigma models.

Abstract

We apply the event-chain algorithm proposed by Bernard, Krauth and Wilson in 2009 to toy models of lattice QCD. We give a formal prove of stability of the algorithm. We study its performance at the example of the massive Gaussian model on the square and the simple cubic lattice, the $O(3)$-invariant non-linear $\sigma$-model and the $SU(3) \times SU(3)$ principle chiral model on the square lattice. In all these cases we find that critical slowing down is essentially eliminated.