Testing the event-chain algorithm in asymptotically free models

We apply the event-chain algorithm proposed by Bernard et al. in 2009 to toy models of lattice QCD. We give a formal proof 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 nonlinear $\sigma$-model on the square lattice, and the $SU(3)\times SU(3)$ principal chiral model on the square lattice. In all these cases we find that critical slowing down is essentially eliminated.

Figure 1

Integrated autocorrelation time for the observable $O_3$, left the two-dimensional Gaussian model, right the three-dimensional version. The integrated autocorrelation times are given in units of $L^d$.

Figure 2

Integrated autocorrelation time of the susceptibility as a function of the average number of events within one update sequence divided by the lattice volume. One the left/right we give the results for the fundamental/adjoint representation. In both cases, we observe a weak dependence on the length of the sequence and a shallow minimum.

Figure 3

Scaling of the integrated autocorrelation times with the correlation length. We observe dynamical critical exponents $z$ well below 1 in all cases.