A hierarchy of accelerated Monte Carlo algorithms was presented which could be used to investigate the kinetic evolution of systems consisting of interacting defects or impurities in a solid matrix. Local models were used to approximate the interactions among particles and a specific application of the algorithms to the study of vacancy agglomeration was presented. It was shown that an extension of the Ising model, including an effective second neighbor interaction, gave a vacancy clusters energetics in good agreement with some quantum mechanical calculations. The accelerate algorithms implemented allow to speed up the calculations avoiding the bottlenecks which occurred when the standard Metropolis algorithm was applied. These bottlenecks were due to the huge amount of rejected transition attempts and to the rapid fluctuations between quasi-degenerate configurations. The equivalence between the results obtained using standard and accelerated algorithms was demonstrated. The gain in CPU time when the algorithms were applied to two different vacancy interaction models was considered in detail. In the case of a simple Ising model an optimized code which was some 105 times faster than the standard Metropolis could be implemented. When the extended interaction was considered, the gain reduced to some 103. Therefore the gain in speed, achievable with accelerate codes, was strongly dependent on the kinetic features of the interaction models. Indeed a relevant consequence of the second neighbor interaction was the migration of the aggregates which boosts the agglomeration process. This faster agglomeration reduces the effects of bottlenecks during the ripening process thus reducing the difference in efficiency between accelerated and conventional codes.

Accelerated Monte Carlo Algorithms for Defect Diffusion and Clustering. A.La Magna, S.Coffa: Computational Materials Science, 2000, 17[1], 21-33