AVERAGE SQUARE ATOMIC DISPLACEMENT - A COMPARISON OF THE MONTE-CARLO AND GREENS-FUNCTION RESULTS

Highly accurate results for the mean-square displacement (MSD) of an a tom for a nearest-neighbor Lennard-Jones model of a f.c.c. solid are p resented. These results are obtained from the Monte-Carlo (MC) method and the Green's function method. The dependence of MSD on the sample s ize (N) in the MC method and similarly the dependence of PI MSD on the number of wave vectors used in the calculation by the Green's functio n method is discussed in detail. The results are presented by both met hods for the infinite sample size limit as well as for the finite size s, i.e., 32-, 108-, and 256-atom sample sizes and the same number of c orresponding wave vectors. It is shown that an analytical method like the Green's function method reproduces almost exactly the results of t he MC method (a completely numerical procedure) for all temperatures e xcept at the melting point (T-m). The computing time required in the f ormer method is only a fraction of the latter one.