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