PPT Slide
The Monte Carlo algorithm employed in this work is different from the classical Metropolis procedure [28]. Besides the ordinary Metropolis random walk move with step ?, swapping of particles of different species is performed at random. Namely, at each step a particle and a random number R, which is equally distributed on (0,1) is chosen. If Rɘ.5 then Metropolis random walk move is attempted. If R?0.5 the particle is attempted to be swapped with another particle, which is chosen randomly from all particles of unlike species. The Metropolis step (D) is controlled in such a way that the acceptance ratio of the Metropolis walks is in the range from (0.4; 0.6) (more exactly: after a cycle over all particles the acceptance ratio is checked. If it appears to be less than 0.4 D is decreased, if it happens to be greater than 0.6 D is increased).
We also compute the swapping acceptance ratio, but it is not controlled. Swapping enormously increases the speed of equilibration of the system, especially at high densities (which are of interest when a is small). It also eliminates the danger for the particles of being "locked" among each other, as it may be the case for the standard Metropolis walk. It also gives an opportunity to consider the demixing transition for crystalline structures - the opportunity that was completely excluded in a number of previous investigations [21-23].
In order to increase the speed of computations, a neighbor list has been employed. Before this improvement the computer time was scaling with the total number of particles (N) as tCPU=O(N2). The neighbor list enables to achieve tCPU=O(N).
The program source code is in appendix A.