Surface crossover exponent for branched polymers in two dimensions

Transfer-matrix methods on finite-width strips with free boundary conditions are applied to lattice site animals, which provide a model for randomly branched polymers in a good solvent. By assigning a distinct fugacity to sites along the strip edges, critical properties at the special (adsorption) and ordinary transitions are assessed. The crossover exponent at the adsorption point is estimated as $\phi = 0.505 \pm 0.015$, consistent with recent predictions that $\phi = 1/2$ exactly for all space dimensionalities.Comment: 10 pages, LaTeX with Institute of Physics macros, to appear in Journal of Physics

Correlation decay and conformal anomaly in the two-dimensional random-bond Ising ferromagnet

The two-dimensional random-bond Ising model is numerically studied on long strips by transfer-matrix methods. It is shown that the rate of decay of correlations at criticality, as derived from averages of the two largest Lyapunov exponents plus conformal invariance arguments, differs from that obtained through direct evaluation of correlation functions. The latter is found to be, within error bars, the same as in pure systems. Our results confirm field-theoretical predictions. The conformal anomaly $c$ is calculated from the leading finite-width correction to the averaged free energy on strips. Estimates thus obtained are consistent with $c=1/2$, the same as for the pure Ising model.Comment: RevTeX 3, 11 pages +2 figures, uuencoded, IF/UFF preprin

Location of the Multicritical Point for the Ising Spin Glass on the Triangular and Hexagonal Lattices

A conjecture is given for the exact location of the multicritical point in the phase diagram of the +/- J Ising model on the triangular lattice. The result p_c=0.8358058 agrees well with a recent numerical estimate. From this value, it is possible to derive a comparable conjecture for the exact location of the multicritical point for the hexagonal lattice, p_c=0.9327041, again in excellent agreement with a numerical study. The method is a variant of duality transformation to relate the triangular lattice directly with its dual triangular lattice without recourse to the hexagonal lattice, in conjunction with the replica method.Comment: 9 pages, 1 figure; Minor corrections in notatio

On weak vs. strong universality in the two-dimensional random-bond Ising ferromagnet

We address the issue of universality in two-dimensional disordered Ising systems, by considering long, finite-width strips of ferromagnetic Ising spins with randomly distributed couplings. We calculate the free energy and spin-spin correlation functions (from which averaged correlation lengths, $\xi^{ave}$, are computed) by transfer-matrix methods. An {\it ansatz} for the size-dependence of logarithmic corrections to $\xi^{ave}$ is proposed. Data for both random-bond and site-diluted systems show that pure system behaviour (with $\nu=1$) is recovered if these corrections are incorporated, discarding the weak--universality scenario.Comment: RevTeX code, 4 pages plus 2 Postscript figures; to appear in Physical Review B Rapid Communication

A new eriophyoid mite species (Acari: Eriophyoidea) damaging Eucalyptus wandoo in Western Australia.

Resumo

Genomic islands of divergence in the Yellow Tang and the Brushtail Tang Surgeonfishes.

The current ease of obtaining thousands of molecular markers challenges the notion that full phylogenetic concordance, as proposed by phylogenetic species concepts, is a requirement for defining species delimitations. Indeed, the presence of genomic islands of divergence, which may be the cause, or in some cases the consequence, of speciation, precludes concordance. Here, we explore this issue using thousands of RAD markers on two sister species of surgeonfishes (Teleostei: Acanthuridae), Zebrasoma flavescens and Z. scopas, and several populations within each species. Species are readily distinguished based on their colors (solid yellow and solid brown, respectively), yet populations and species are neither distinguishable using mitochondrial markers (cytochrome c oxidase 1), nor using 5193 SNPs (pairwise Φst = 0.034). In contrast, when using outlier loci, some of them presumably under selection, species delimitations, and strong population structure follow recognized taxonomic positions (pairwise Φst = 0.326). Species and population delimitation differences based on neutral and selected markers are likely due to local adaptation, thus being consistent with the idea that these genomic islands of divergence arose as a consequence of isolation. These findings, which are not unique, raise the question of a potentially important pathway of divergence based on local adaptation that is only evident when looking at thousands of loci

Scaling and finte-size-scaling in the two dimensional random-coupling Ising ferromagnet

It is shown by Monte Carlo method that the finite size scaling (FSS) holds in the two dimensional random-coupled Ising ferromagnet. It is also demonstrated that the form of universal FSS function constructed via novel FSS scheme depends on the strength of the random coupling for strongly disordered cases. Monte Carlo measurements of thermodynamic (infinite volume limit) data of the correlation length ($\xi$) up to $\xi \simeq 200$ along with measurements of the fourth order cumulant ratio (Binder's ratio) at criticality are reported and analyzed in view of two competing scenarios. It is demonstrated that the data are almost exclusively consistent with the scenario of weak universality.Comment: 9 pages, 4figuer

On surface properties of two-dimensional percolation clusters

The two-dimensional site percolation problem is studied by transfer-matrix methods on finite-width strips with free boundary conditions. The relationship between correlation-length amplitudes and critical indices, predicted by conformal invariance, allows a very precise determination of the surface decay-of-correlations exponent, $\eta_s = 0.6664 \pm 0.0008$, consistent with the analytical value $\eta_s = 2/3$. It is found that a special transition does not occur in the case, corroborating earlier series results. At the ordinary transition, numerical estimates are consistent with the exact value $y_s = -1$ for the irrelevant exponent.Comment: 8 pages, LaTeX with Institute of Physics macros, to appear in Journal of Physics

Failure of single-parameter scaling of wave functions in Anderson localization

We show how to use properties of the vectors which are iterated in the transfer-matrix approach to Anderson localization, in order to generate the statistical distribution of electronic wavefunction amplitudes at arbitary distances from the origin of $L^{d-1} \times \infty$ disordered systems. For $d=1$ our approach is shown to reproduce exact diagonalization results available in the literature. In $d=2$, where strips of width $L \leq 64$ sites were used, attempted fits of gaussian (log-normal) forms to the wavefunction amplitude distributions result in effective localization lengths growing with distance, contrary to the prediction from single-parameter scaling theory. We also show that the distributions possess a negative skewness $S$, which is invariant under the usual histogram-collapse rescaling, and whose absolute value increases with distance. We find $0.15 \lesssim -S \lesssim 0.30$ for the range of parameters used in our study, .Comment: RevTeX 4, 6 pages, 4 eps figures. Phys. Rev. B (final version, to be published