Fast recall of state-history in kinetic Monte Carlo simulations utilizing the Zobrist key

We present a novel application of the Zobrist hashing method, known in the computer chess literature, to simulation of diffusional phase transformations in metal alloys. A history of previously visited states can be easily maintained, allowing very fast lookup of energies and transition rates calculated earlier in the simulation. The method has been applied to the simulation of a Fe-1at.%Cu system, with simple potentials and a transition rate for diffusional events approximated from the difference in internal energy between trial states. In this simple model at temperatures of 1073 K we find that 61.2% of the states considered during the simulation have been seen previously, and that this proportion rises to 85.1% at 773 K and even to 99.9% at 373 K. Rapid recall of these states reduces the computational time taken for the same sequence of atom-vacancy exchange moves by a factor of 6.3 at 773 K rising to over 100 at 373 K. We suggest that a similar speedup factor will be found using more sophisticated models of diffusion and that the method can, with small modifications, be applied to a wide range of kinetic Monte Carlo simulations of atomistic diffusion processes.