Suppressing correlations in massively parallel simulations of lattice models

For lattice Monte Carlo simulations parallelization is crucial to make studies of large systems and long simulation time feasible, while sequential simulations remain the gold-standard for correlation-free dynamics. Here, various domain decomposition schemes are compared, concluding with one which delivers virtually correlation-free simulations on GPU Extensive simulations of the octahedron model for $2+1$ dimensional Karda--Parisi--Zhang surface growth, which is very sensitive to correlation in the site-selection dynamics, were performed to show self-consistency of the parallel runs and agreement with the sequential algorithm. We present a GPU implementation providing a speedup of about $30\times$ over a parallel CPU implementation on a single socket and at least $180\times$ with respect to the sequential reference.