Comment on ``Scaling Laws for a System with Long-Range Interactions within Tsallis Statistics''

In their recent Letter [Phys. Rev. Lett. 83, 4233 (1999)], Salazar and Toral (ST) study numerically a finite Ising chain with non-integrable interactions decaying like 1/r^(d+sigma) where -d <= sigma <= 0 (like ST, we discuss general dimensionality d). In particular, they explore a presumed connection between non-integrable interactions and Tsallis's non-extensive statistics. We point out that (i) non-integrable interactions provide no more motivation for Tsallis statistics than do integrable interactions, i.e., Gibbs statistics remain meaningful for the non-integrable case, and in fact provide a {\em complete and exact treatment}; and (ii) there are undesirable features of the method ST use to regulate the non-integrable interactions.Comment: Accepted for publication in Phys. Rev. Let

Single-Species Three-Particle Reactions in One Dimension

Renormalization group calculations for fluctuation-dominated reaction-diffusion systems are generally in agreement with simulations and exact solutions. However, simulations of the single-species reactions 3A->(0,A,2A) at their upper critical dimension d_c=1 have found asymptotic densities argued to be inconsistent with renormalization group predictions. We show that this discrepancy is resolved by inclusion of the leading corrections to scaling, which we derive explicitly and show to be universal, a property not shared by the A+A->(0,A) reactions. Finally, we demonstrate that two previous Smoluchowski approaches to this problem reduce, with various corrections, to a single theory which yields, surprisingly, the same asymptotic density as the renormalization group.Comment: 8 pages, 5 figs, minor correction

Local Electronic and Magnetic Studies of an Artificial La2FeCrO6 Double Perovskite

Through the utilization of element-resolved polarized x-ray probes, the electronic and magnetic state of an artificial La2FeCrO6 double perovskite were explored. Applying unit-cell level control of thin film growth on SrTiO3 (111), the rock salt double perovskite structure can be created for this system, which does not have an ordered perovskite phase in the bulk. We find that the Fe and Cr are in the proper 3+ valence state, but, contrary to previous studies, the element-resolved magnetic studies find the moments in field are small and show no evidence of a sizable magnetic moment in the remanent state.Comment: 3 pages, 4 figure

Scaling of Reaction Zones in the A+B->0 Diffusion-Limited Reaction

We study reaction zones in three different versions of the A+B->0 system. For a steady state formed by opposing currents of A and B particles we derive scaling behavior via renormalization group analysis. By use of a previously developed analogy, these results are extended to the time-dependent case of an initially segregated system. We also consider an initially mixed system, which forms reaction zones for dimension d<4. In this case an extension of the steady-state analogy gives scaling results characterized by new exponents.Comment: 4 pages, REVTeX 3.0 with epsf, 2 uuencoded postscript figures appended, OUTP-94-33

Fast and Accurate Coarsening Simulation with an Unconditionally Stable Time Step

We present Cahn-Hilliard and Allen-Cahn numerical integration algorithms that are unconditionally stable and so provide significantly faster accuracy-controlled simulation. Our stability analysis is based on Eyre's theorem and unconditional von Neumann stability analysis, both of which we present. Numerical tests confirm the accuracy of the von Neumann approach, which is straightforward and should be widely applicable in phase-field modeling. We show that accuracy can be controlled with an unbounded time step Delta-t that grows with time t as Delta-t ~ t^alpha. We develop a classification scheme for the step exponent alpha and demonstrate that a class of simple linear algorithms gives alpha=1/3. For this class the speed up relative to a fixed time step grows with the linear size of the system as N/log N, and we estimate conservatively that an 8192^2 lattice can be integrated 300 times faster than with the Euler method.Comment: 14 pages, 6 figure

Surface Enhanced Raman Spectroscopy of Organic Molecules on Magnetite (Fe_3O_4) Nanoparticles

Surface-enhanced Raman spectroscopy (SERS) of species bound to environmentally relevant oxide nanoparticles is largely limited to organic molecules structurally related to catechol that facilitate a chemical enhancement of the Raman signal. Here, we report that magnetite (Fe_3O_4) nanoparticles provide a SERS signal from oxalic acid and cysteine via an electric field enhancement. Magnetite thus likely provides an oxide substrate for SERS study of any adsorbed organic molecule. This substrate combines benefits from both metal-based and chemical SERS by providing an oxide surface for studies of environmentally and catalytically relevant detailed chemical bonding information with fewer restrictions of molecular structure or binding mechanisms. Therefore, the magnetite-based SERS demonstrated here provides a new approach to establishing the surface interactions of environmentally relevant organic ligands and mineral surfaces