Lattice Monte Carlo Methods
Mykyta Chubynsky
Monte Carlo simulations on a lattice provide a faster alternative to continuum Monte Carlo methods and Molecular Dynamics, but are generally less accurate. For the simple case of simulations of diffusion of point particles, we have shown that introducing the possibility for the particle to stay put at a given step of the algorithm and reducing the time step accordingly can increase the accuracy of the simulation and that for a given lattice step there is a value of the time step for which the accuracy of the algorithm is optimal. This may make it possible to increase the accuracy of Lattice Monte Carlo methods and make them more competitive compared to the alternatives.
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