Bit Level Correlations in Some Pseudorandom Number Generators

We present results of extensive bit level tests on some pseudorandom number generators which are commonly used in physics applications. The generators have first been tested with an extended version of the $d$-tuple test. Second, we have developed a novel {\it cluster test} where a physical analogy of the binary numbers with the two dimensional Ising model has been utilized. We demonstrate that the new test is rather powerful in finding periodic correlations on bit level. Results of both test methods are presented for each bit of the output of the generators. Some generators exhibit clear bit level correlations but we find no evidence of discernible correlations for generators, which have recently produced systematic errors in Monte Carlo simulations.Comment: University of Helsinki preprint HU-TFT-93-4

Geometric Random Inner Products: A New Family of Tests for Random Number Generators

We present a new computational scheme, GRIP (Geometric Random Inner Products), for testing the quality of random number generators. The GRIP formalism utilizes geometric probability techniques to calculate the average scalar products of random vectors generated in geometric objects, such as circles and spheres. We show that these average scalar products define a family of geometric constants which can be used to evaluate the quality of random number generators. We explicitly apply the GRIP tests to several random number generators frequently used in Monte Carlo simulations, and demonstrate a new statistical property for good random number generators

Non-Arrhenius Behavior of Surface Diffusion Near a Phase Transition Boundary

We study the non-Arrhenius behavior of surface diffusion near the second-order phase transition boundary of an adsorbate layer. In contrast to expectations based on macroscopic thermodynamic effects, we show that this behavior can be related to the average microscopic jump rate which in turn is determined by the waiting-time distribution W(t) of single-particle jumps at short times. At long times, W(t) yields a barrier that corresponds to the rate-limiting step in diffusion. The microscopic information in W(t) should be accessible by STM measurements.Comment: 4 pages, Latex with RevTeX macro

Density profile evolution and nonequilibrium effects in partial and full spreading measurements of surface diffusion

We study the nature of nonequilibrium effects in the collective diffusion coefficient DC(θ) vs the coverage θ as extracted from Boltzmann–Matano analysis of spreading coverage profiles. We focus on the temporal behavior of the profiles and study how the corresponding nonequilibrium effects in DC(θ) depend on the initial density gradient and the initial state from which the spreading starts. To this end, we carry out extensive Monte Carlo simulations for a lattice-gas model of the O/W(110) system. Studies of submonolayer spreading from an initially ordered p(2×1) phase at θ=12 reveal that the spreading and diffusion rates in directions parallel and perpendicular to rows of oxygen atoms are significantly different within the ordered phase. Aside from this effect, we find that the degree of ordering in the initial phase has a relatively small impact on the overall behavior of DC(θ). Also, although we find that nonequilibrium effects are clearly present in submonolayer spreading profiles, DC(θ) determined from such data approaches its asymptotic equilibrium behavior much more rapidly than in the case of full spreading. Nevertheless, in both cases there are noticeable deviations from equilibrium results that persist even at very long times and are strongest in ordered phases and in the vicinity of phase boundaries. These conclusions are confirmed by complementary studies of the temporal behavior of the order parameter φ(θ). Finally, we use DC(θ) and φ(θ) to determine the locations of phase boundaries and find such data to be clearly time dependent during full spreading. We conclude that nonequilibrium effects seem to be an inherent feature in profile evolution studies of surface diffusion in all cases where ordering plays a prominent role. This warrants particular care to be taken with profile spreading experiments.Peer reviewe

A Dynamical Mean Field Theory for the Study of Surface Diffusion Constants

We present a combined analytical and numerical approach based on the Mori projection operator formalism and Monte Carlo simulations to study surface diffusion within the lattice-gas model. In the present theory, the average jump rate and the susceptibility factor appearing are evaluated through Monte Carlo simulations, while the memory functions are approximated by the known results for a Langmuir gas model. This leads to a dynamical mean field theory (DMF) for collective diffusion, while approximate correlation effects beyond DMF are included for tracer diffusion. We apply our formalism to three very different strongly interacting systems and compare the results of the new approach with those of usual Monte Carlo simulations. We find that the combined approach works very well for collective diffusion, whereas for tracer diffusion the influence of interactions on the memory effects is more prominent.Comment: 13 pages LaTeX and 6 PostScript figures, style files included. To appear in Surface Science Letter