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

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

Scientific Classification

types: ArticleN/

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

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

Kosterlitz-Thouless transition in three-state mixed Potts ferro-antiferromagnets

We study three-state Potts spins on a square lattice, in which all bonds are ferromagnetic along one of the lattice directions, and antiferromagnetic along the other. Numerical transfer-matrix are used, on infinite strips of width $L$ sites, $4 \leq L \leq 14$. Based on the analysis of the ratio of scaled mass gaps (inverse correlation lengths) and scaled domain-wall free energies, we provide strong evidence that a critical (Kosterlitz-Thouless) phase is present, whose upper limit is, in our best estimate, $T_c=0.29 \pm 0.01$. From analysis of the (extremely anisotropic) nature of excitations below $T_c$, we argue that the critical phase extends all the way down to T=0. While domain walls parallel to the ferromagnetic direction are soft for the whole extent of the critical phase, those along the antiferromagnetic direction seem to undergo a softening transition at a finite temperature. Assuming a bulk correlation length varying, for $T>T_c$, as $\xi (T) =a_\xi \exp [ b_\xi (T-T_c)^{-\sigma}]$, $\sigma \simeq 1/2$, we attempt finite-size scaling plots of our finite-width correlation lengths. Our best results are for $T_c=0.50 \pm 0.01$. We propose a scenario in which such inconsistency is attributed to the extreme narrowness of the critical region.Comment: 11 pages, 6 .eps figures, LaTeX with IoP macros, to be published in J Phys