  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.
