Fluctuations and universality in a catalysis model with long-range reactivity

The critical properties of the Ziff-Gulari-Barshad (ZGB) model with the addition of long-range reactivity [C.H. Chan and P.A. Rikvold, Phys. Rev. E 91, 012103 (2015)] are further investigated. The scaling behaviors of the order parameter, susceptibility, and correlation length provide addi- tional evidence that the universality class of the ZGB system changes from the two-dimensional Ising class to the mean-field class with the addition of even a weak long-range reactivity mechanism

Recent Results on the Decay of Metastable Phases

We review some aspects of current knowledge regarding the decay of metastable phases in many-particle systems. In particular we emphasize recent theoretical and computational developments and numerical results regarding homogeneous nucleation and growth in kinetic Ising and lattice-gas models. An introductory discussion of the droplet theory of homogeneous nucleation is followed by a discussion of Monte Carlo and transfer-matrix methods commonly used for numerical study of metastable decay, including some new algorithms. Next we discuss specific classes of systems. These include a brief discussion of recent progress for fluids, and more exhaustive considerations of ferromagnetic Ising models ({\it i.e.}, attractive lattice-gas models) with weak long-range interactions and with short-range interactions. Whereas weak-long-range-force (WLRF) models have infinitely long-lived metastable phases in the infinite-range limit, metastable phases in short-range-force (SRF) models eventually decay, albeit extremely slowly. Recent results on the finite-size scaling of metastable lifetimes in SRF models are reviewed, and it is pointed out that such effects may be experimentally observable.Comment: 34 pages, LaTex, 8 ps figs. on request, preprint FSU-SCRI-94-6

Soft versus Hard Dynamics for Field-driven Solid-on-Solid Interfaces

Analytical arguments and dynamic Monte Carlo simulations show that the microstructure of field-driven Solid-on-Solid interfaces depends strongly on the dynamics. For nonconservative dynamics with transition rates that factorize into parts dependent only on the changes in interaction energy and field energy, respectively (soft dynamics), the intrinsic interface width is field-independent. For non-factorizing rates, such as the standard Glauber and Metropolis algorithms (hard dynamics), it increases with the field. Consequences for the interface velocity and its anisotropy are discussed.Comment: 9 pages LaTex with imbedded .eps figs. Minor revision

Discrete-Event Analytic Technique for Surface Growth Problems

We introduce an approach for calculating non-universal properties of rough surfaces. The technique uses concepts of distinct surface-configuration classes, defined by the surface growth rule. The key idea is a mapping between discrete events that take place on the interface and its elementary local-site configurations. We construct theoretical probability distributions of deposition events at saturation for surfaces generated by selected growth rules. These distributions are then used to compute measurable physical quantities. Despite the neglect of temporal correlations, our approximate analytical results are in very good agreement with numerical simulations. This discrete-event analytic technique can be particularly useful when applied to quantification problems, which are known to not be suited to continuum methods.Comment: 4 pages, 7 figures, published 17 Feb. 200

Fluctuations and correlations in an individual-based model of biological coevolution

We extend our study of a simple model of biological coevolution to its statistical properties. Staring with a complete description in terms of a master equation, we provide its relation to the deterministic evolution equations used in previous investigations. The stationary states of the mutationless model are generally well approximated by Gaussian distributions, so that the fluctuations and correlations of the populations can be computed analytically. Several specific cases are studied by Monte Carlo simulations, and there is excellent agreement between the data and the theoretical predictions.Comment: 25 pages, 2 figure

Slow Forcing in the Projective Dynamics Method

We provide a proof that when there is no forcing the recently introduced projective dynamics Monte Carlo algorithm gives the exact lifetime of the metastable state, within statistical uncertainties. We also show numerical evidence illustrating that for slow forcing the approach to the zero-forcing limit is rather rapid. The model studied numerically is the 3-dimensional 3-state Potts ferromagnet.Comment: 1 figure, invited submission to CCP'98 conference, submitted to Computer Physics Communication