Testing the event-chain algorithm in asymptotically free models

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.