Universal relations in the finite-size correction terms of two-dimensional Ising models

Quite recently, Izmailian and Hu [Phys. Rev. Lett. 86, 5160 (2001)] studied the finite-size correction terms for the free energy per spin and the inverse correlation length of the critical two-dimensional Ising model. They obtained the universal amplitude ratio for the coefficients of two series. In this study we give a simple derivation of this universal relation; we do not use an explicit form of series expansion. Moreover, we show that the Izmailian and Hu's relation is reduced to a simple and exact relation between the free energy and the correlation length. This equation holds at any temperature and has the same form as the finite-size scaling.Comment: 4 pages, RevTeX, to appear in Phys. Rev. E, Rapid Communication

Spanning forests and the q-state Potts model in the limit q \to 0

We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially, this limit gives rise to the generating polynomial of spanning forests; physically, it provides information about the Potts-model phase diagram in the neighborhood of (q,v) = (0,0). We have studied this model on the square and triangular lattices, using a transfer-matrix approach at both real and complex values of w. For both lattices, we have computed the symbolic transfer matrices for cylindrical strips of widths 2 \le L \le 10, as well as the limiting curves of partition-function zeros in the complex w-plane. For real w, we find two distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp. w_0 = -0.1753 \pm 0.0002) for the square (resp. triangular) lattice. For w > w_0 we find a non-critical disordered phase, while for w < w_0 our results are compatible with a massless Berker-Kadanoff phase with conformal charge c = -2 and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w = w_0 we find a "first-order critical point": the first derivative of the free energy is discontinuous at w_0, while the correlation length diverges as w \downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0 seems to be the same for both lattices and it differs from that of the Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1, the leading thermal scaling dimension is x_{T,1} = 0, and the critical exponents are \nu = 1/d = 1/2 and \alpha = 1.Comment: 131 pages (LaTeX2e). Includes tex file, three sty files, and 65 Postscript figures. Also included are Mathematica files forests_sq_2-9P.m and forests_tri_2-9P.m. Final journal versio

Population connectivity of the highly migratory shortfin mako (Isurus oxyrinchus Rafinesque 1810) and implications for management in the Southern Hemisphere

Published: 20 November 2018In this paper we combine analyses of satellite telemetry and molecular data to investigate spatial connectivity and genetic structure among populations of shortfin mako (Isurus oxyrinchus) in and around Australian waters, where this species is taken in recreational and commercial fisheries. Mitochondrial DNA data suggest matrilineal substructure across hemispheres, while nuclear DNA data indicate shortfin mako may constitute a globally panmictic population. There was generally high genetic connectivity within Australian waters. Assessing genetic connectivity across the Indian Ocean basin, as well as the extent that shortfin mako exhibit sex biases in dispersal patterns would benefit from future improved sampling of adult size classes, particularly of individuals from the eastern Indian Ocean. Telemetry data indicated that Australasian mako are indeed highly migratory and frequently make long-distance movements. However, individuals also exhibit fidelity to relatively small geographic areas for extended periods. Together these patterns suggest that shortfin mako populations may be genetically homogenous across large geographical areas as a consequence of few reproductively active migrants, although spatial partitioning exists. Given that connectivity appears to occur at different scales, management at both the national and regional levels seems most appropriate.Shannon Corrigan, Andrew D. Lowther, Luciano B. Beheregaray, Barry D. Bruce, Geremy Cliff, Clinton A. Duffy, Alan Foulis, Malcolm P. Francis, Simon D. Goldsworthy, John R. Hyde, Rima W. Jabado, Dovi Kacev, Lindsay Marshall, Gonzalo R. Mucientes, Gavin J. P. Naylor, Julian G. Pepperell, Nuno Queiroz, William T. White, Sabine P. Wintner and Paul J. Roger

Contribuição à biologia de serpentes da Bahia, Brasil: I. vivíparas Contribution to reproductive biology of snakes in Bahia, Brazil: I. viviparous

<abstract language="eng">Great part of lhe avaiable data about snakes reprodution refers to species coming from subtropical and temperate regions. In Brazil, the data is rather rare and can be found in various works where information is restricted. Results from studies developed with five viviparous snakes - Crotalus durissus cascavella (Wagler, 1824). Bothrops erythromelas(Amaral, 1923), B. leucurus (Wagler, 1824), Helicops leopardinus (Schlegel, 1873) and Thamnodynastes strigilis (Thiinberg, 1787) - which come from the Northeast of Brazil (Bahia) are described. Data about pregnancy and birth, number, sex ratio, length and weight of neonates is given and discussed