Parallel Monte Carlo Simulations of Dipolar Systems: A New Approach to Accelerate the Potential Evaluation

The Monte Carlo-Metropolis (MM) and Molecular Dynamics (MD) techniques are among the most popular approaches to describe interacting particle systems [1]. While the former evaluates the potential arising from the particle interactions by identifying a number of statistically significative configurations, the latter requires the computation of the deterministic force field in the system. In both cases a quadratic relationship among the computing time and the number N of particles is established (O(N2)). The computational load is very high, since simulations consist of a high number of cycles to achieve a meaningful description of the physical system examined. In the physical systems we considered, periodic boundary conditions and minimum image conventions are applied, together with the Ewald method for summing the interactions between a particle and all the periodic images of the other. Even by choosing the parameters of the method in order to obtain a fixed accuracy and to minimize the computation time, however, it scales with O(N3/2), but remains still high [2][3]. Thus, due to the strong dependence of the computing time on the number of particles, only long simulations are able to describe complex systems. A useful solution can be found in the use of look-up tables, where the potentials or forces are evaluated for particles located on fixed points of a 2D or 3D grid, at the beginning of the simulation. Afterwards, the potentials or force fields due to particles, not located on the grid, are more quickly obtained by interpolation of the originally tabulated values, without losing accuracy. MM Simulations have been carried out, yielding encouraging results. Moreover, the speed-up achieved can be even greater if the algorithm is parallelised on a multiprocessor system. The overall speed-up achieved reaches a few thousands for a system with 1000 dipoles and it is well scalable with the dipole number. This makes feasible simulations which otherwise could take unacceptable execution times