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An extension of the synchronous parallel kinetic Monte Carlo (pkMC) algorithmdeveloped by Martinez {\it et al} [{\it J.\ Comp.\ Phys.} {\bf 227} (2008)3804] to discrete lattices is presented. The method solves the master equationsynchronously by recourse to null events that keep all processors time clockscurrent in a global sense. Boundary conflicts are rigorously solved by adoptinga chessboard decomposition into non-interacting sublattices. We find that thebias introduced by the spatial correlations attendant to the sublatticedecomposition is within the standard deviation of the serial method, whichconfirms the statistical validity of the method. We have assessed the parallelefficiency of the method and find that our algorithm scales consistently withproblem size and sublattice partition. We apply the method to the calculationof scale-dependent critical exponents in billion-atom 3D Ising systems, withvery good agreement with state-of-the-art multispin simulations.

Billion-atom Synchronous Parallel Kinetic Monte Carlo Simulations of Critical 3D Ising Systems