The instability of Alexander-McTague crystals and its implication for nucleation

We show that the argument of Alexander and McTague, that the bcc crystalline structure is favored in those crystallization processes where the first order character is not too pronounced, is not correct. We find that any solution that satisfies the Alexander-McTague condition is not stable. We investigate the implication of this result for nucleation near the pseudo- spinodal in near-meanfield systems.Comment: 20 pages, 0 figures, submitted to Physical Review

Nucleation in Systems with Elastic Forces

Systems with long-range interactions when quenced into a metastable state near the pseudo-spinodal exhibit nucleation processes that are quite different from the classical nucleation seen near the coexistence curve. In systems with long-range elastic forces the description of the nucleation process can be quite subtle due to the presence of bulk/interface elastic compatibility constraints. We analyze the nucleation process in a simple 2d model with elastic forces and show that the nucleation process generates critical droplets with a different structure than the stable phase. This has implications for nucleation in many crystal-crystal transitions and the structure of the final state

Phase Transitions in a Two-Component Site-Bond Percolation Model

A method to treat a N-component percolation model as effective one component model is presented by introducing a scaled control variable $p_{+}$. In Monte Carlo simulations on $16^{3}$, $32^{3}$, $64^{3}$ and $128^{3}$ simple cubic lattices the percolation threshold in terms of $p_{+}$ is determined for N=2. Phase transitions are reported in two limits for the bond existence probabilities $p_{=}$ and $p_{\neq}$. In the same limits, empirical formulas for the percolation threshold $p_{+}^{c}$ as function of one component-concentration, $f_{b}$, are proposed. In the limit $p_{=} = 0$ a new site percolation threshold, $f_{b}^{c} \simeq 0.145$, is reported.Comment: RevTeX, 5 pages, 5 eps-figure

Simulations of grafted polymers in a good solvent

We present improved simulations of three-dimensional self avoiding walks with one end attached to an impenetrable surface on the simple cubic lattice. This surface can either be a-thermal, having thus only an entropic effect, or attractive. In the latter case we concentrate on the adsorption transition, We find clear evidence for the cross-over exponent to be smaller than 1/2, in contrast to all previous simulations but in agreement with a re-summed field theoretic $\epsilon$-expansion. Since we use the pruned-enriched Rosenbluth method (PERM) which allows very precise estimates of the partition sum itself, we also obtain improved estimates for all entropic critical exponents.Comment: 5 pages with 9 figures included; minor change

Dynamic Critical Behavior of the Swendsen-Wang Algorithm: The Two-Dimensional 3-State Potts Model Revisited

We have performed a high-precision Monte Carlo study of the dynamic critical behavior of the Swendsen-Wang algorithm for the two-dimensional 3-state Potts model. We find that the Li-Sokal bound ($\tau_{int,E} \geq const \times C_H$) is almost but not quite sharp. The ratio $\tau_{int,E} / C_H$ seems to diverge either as a small power ($\approx 0.08$) or as a logarithm.Comment: 35 pages including 3 figures. Self-unpacking file containing the LaTeX file, the needed macros (epsf.sty, indent.sty, subeqnarray.sty, and eqsection.sty) and the 3 Postscript figures. Revised version fixes a normalization error in \xi (with many thanks to Wolfhard Janke for finding the error!). To be published in J. Stat. Phys. 87, no. 1/2 (April 1997

Superdiffusion in a Model for Diffusion in a Molecularly Crowded Environment

We present a model for diffusion in a molecularly crowded environment. The model consists of random barriers in percolation network. Random walks in the presence of slowly moving barriers show normal diffusion for long times, but anomalous diffusion at intermediate times. The effective exponents for square distance versus time usually are below one at these intermediate times, but can be also larger than one for high barrier concentrations. Thus we observe sub- as well as super-diffusion in a crowded environment.Comment: 8 pages including 4 figure

Clusters and Fluctuations at Mean-Field Critical Points and Spinodals

We show that the structure of the fluctuations close to spinodals and mean-field critical points is qualitatively different than the structure close to non-mean-field critical points. This difference has important implications for many areas including the formation of glasses in supercooled liquids. In particular, the divergence of the measured static structure function in near-mean-field systems close to the glass transition is suppressed relative to the mean-field prediction in systems for which a spatial symmetry is broken.Comment: 5 pages, 1 figur

Domain Growth and Finite-Size-Scaling in the Kinetic Ising Model

This paper describes the application of finite-size scaling concepts to domain growth in systems with a non-conserved order parameter. A finite-size scaling ansatz for the time-dependent order parameter distribution function is proposed, and tested with extensive Monte-Carlo simulations of domain growth in the 2-D spin-flip kinetic Ising model. The scaling properties of the distribution functions serve to elucidate the configurational self-similarity that underlies the dynamic scaling picture. Moreover, it is demonstrated that the application of finite-size-scaling techniques facilitates the accurate determination of the bulk growth exponent even in the presence of strong finite-size effects, the scale and character of which are graphically exposed by the order parameter distribution function. In addition it is found that one commonly used measure of domain size--the scaled second moment of the magnetisation distribution--belies the full extent of these finite-size effects.Comment: 13 pages, Latex. Figures available on request. Rep #9401

Dynamical Phases of Driven Vortices Interacting with Periodic Pinning

The finite temperature dynamical phases of vortices in films driven by a uniform force and interacting with the periodic pinning potential of a square lattice of columnar defects are investigated by Langevin dynamics simulations of a London model. Vortices driven along the [0,1] direction and at densities for which there are more vortices than columnar defects ($B>B_{\phi}$) are considered. At low temperatures, two new dynamical phases, elastic flow and plastic flow, and a sharp transition between them are identified and characterized according to the behavior of the vortex spatial order, velocity distribution and frequency-dependent velocity correlationComment: 4 pages with 4 figures. To be published in Phys. Rev. B Rapid Communication