Critical Temperature and Amplitude Ratios from a Finite-Temperature Renormalization Group

We study \l\f^4 theory using an environmentally friendly finite-temperature renormalization group. We derive flow equations, using a fiducial temperature as flow parameter, develop them perturbatively in an expansion free from ultraviolet and infrared divergences, then integrate them numerically from zero to temperatures above the critical temperature. The critical temperature, at which the mass vanishes, is obtained by integrating the flow equations and is determined as a function of the zero-temperature mass and coupling. We calculate the field expectation value and minimum of the effective potential as functions of temperature and derive some universal amplitude ratios which connect the broken and symmetric phases of the theory. The latter are found to be in good agreement with those of the three-dimensional Ising model obtained from high- and low-temperature series expansions.Comment: 14 pages of LaTeX. Postscript figures available upon request form [email protected]

The Specific Heat of a Ferromagnetic Film.

We analyze the specific heat for the $O(N)$ vector model on a $d$-dimensional film geometry of thickness $L$ using ``environmentally friendly'' renormalization. We consider periodic, Dirichlet and antiperiodic boundary conditions, deriving expressions for the specific heat and an effective specific heat exponent, \alpha\ef. In the case of $d=3$, for $N=1$, by matching to the exact exponent of the two dimensional Ising model we capture the crossover for \xi_L\ra\infty between power law behaviour in the limit {L\over\xi_L}\ra\infty and logarithmic behaviour in the limit {L\over\xi_L}\ra0 for fixed $L$, where $\xi_L$ is the correlation length in the transverse dimensions.Comment: 21 pages of Plain TeX. Postscript figures available upon request from [email protected]

Explanation and Elaboration Document for the STROBE-Vet Statement: Strengthening the Reporting of Observational Studies in Epidemiology—Veterinary Extension

The STROBE (Strengthening the Reporting of Observational Studies in Epidemiology) statement was first published in 2007 and again in 2014. The purpose of the original STROBE was to provide guidance for authors, reviewers and editors to improve the comprehensiveness of reporting; however, STROBE has a unique focus on observational studies. Although much of the guidance provided by the original STROBE document is directly applicable, it was deemed useful to map those statements to veterinary concepts, provide veterinary examples and highlight unique aspects of reporting in veterinary observational studies. Here, we present the examples and explanations for the checklist items included in the STROBE-Vet Statement. Thus, this is a companion document to the STROBE-Vet Statement Methods and process document, which describes the checklist and how it was developed

The Influence of Thermal Pressure on Equilibrium Models of Hypermassive Neutron Star Merger Remnants

The merger of two neutron stars leaves behind a rapidly spinning hypermassive object whose survival is believed to depend on the maximum mass supported by the nuclear equation of state, angular momentum redistribution by (magneto-)rotational instabilities, and spindown by gravitational waves. The high temperatures (~5-40 MeV) prevailing in the merger remnant may provide thermal pressure support that could increase its maximum mass and, thus, its life on a neutrino-cooling timescale. We investigate the role of thermal pressure support in hypermassive merger remnants by computing sequences of spherically-symmetric and axisymmetric uniformly and differentially rotating equilibrium solutions to the general-relativistic stellar structure equations. Using a set of finite-temperature nuclear equations of state, we find that hot maximum-mass critically spinning configurations generally do not support larger baryonic masses than their cold counterparts. However, subcritically spinning configurations with mean density of less than a few times nuclear saturation density yield a significantly thermally enhanced mass. Even without decreasing the maximum mass, cooling and other forms of energy loss can drive the remnant to an unstable state. We infer secular instability by identifying approximate energy turning points in equilibrium sequences of constant baryonic mass parametrized by maximum density. Energy loss carries the remnant along the direction of decreasing gravitational mass and higher density until instability triggers collapse. Since configurations with more thermal pressure support are less compact and thus begin their evolution at a lower maximum density, they remain stable for longer periods after merger.Comment: 20 pages, 12 figures. Accepted for publication in Ap

Camera trap arrays improve detection probability of wildlife: Investigating study design considerations using an empirical dataset.

Camera trapping is a standard tool in ecological research and wildlife conservation. Study designs, particularly for small-bodied or cryptic wildlife species often attempt to boost low detection probabilities by using non-random camera placement or baited cameras, which may bias data, or incorrectly estimate detection and occupancy. We investigated the ability of non-baited, multi-camera arrays to increase detection probabilities of wildlife. Study design components were evaluated for their influence on wildlife detectability by iteratively parsing an empirical dataset (1) by different sizes of camera arrays deployed (1-10 cameras), and (2) by total season length (1-365 days). Four species from our dataset that represented a range of body sizes and differing degrees of presumed detectability based on life history traits were investigated: white-tailed deer (Odocoileus virginianus), bobcat (Lynx rufus), raccoon (Procyon lotor), and Virginia opossum (Didelphis virginiana). For all species, increasing from a single camera to a multi-camera array significantly improved detection probability across the range of season lengths and number of study sites evaluated. The use of a two camera array increased survey detection an average of 80% (range 40-128%) from the detection probability of a single camera across the four species. Species that were detected infrequently benefited most from a multiple-camera array, where the addition of up to eight cameras produced significant increases in detectability. However, for species detected at high frequencies, single cameras produced a season-long (i.e, the length of time over which cameras are deployed and actively monitored) detectability greater than 0.75. These results highlight the need for researchers to be critical about camera trap study designs based on their intended target species, as detectability for each focal species responded differently to array size and season length. We suggest that researchers a priori identify target species for which inference will be made, and then design camera trapping studies around the most difficult to detect of those species

Dimensional Crossover in the Large N Limit

We consider dimensional crossover for an $O(N)$ Landau-Ginzburg-Wilson model on a $d$-dimensional film geometry of thickness $L$ in the large $N$-limit. We calculate the full universal crossover scaling forms for the free energy and the equation of state. We compare the results obtained using ``environmentally friendly'' renormalization with those found using a direct, non-renormalization group approach. A set of effective critical exponents are calculated and scaling laws for these exponents are shown to hold exactly, thereby yielding non-trivial relations between the various thermodynamic scaling functions.Comment: 25 pages of PlainTe

'Schwinger Model' on the Fuzzy Sphere

In this paper, we construct a model of spinor fields interacting with specific gauge fields on fuzzy sphere and analyze the chiral symmetry of this 'Schwinger model'. In constructing the theory of gauge fields interacting with spinors on fuzzy sphere, we take the approach that the Dirac operator $D_q$ on q-deformed fuzzy sphere $S_{qF}^2$ is the gauged Dirac operator on fuzzy sphere. This introduces interaction between spinors and specific one parameter family of gauge fields. We also show how to express the field strength for this gauge field in terms of the Dirac operators $D_q$ and $D$ alone. Using the path integral method, we have calculated the $2n-$point functions of this model and show that, in general, they do not vanish, reflecting the chiral non-invariance of the partition function.Comment: Minor changes, typos corrected, 18 pages, to appear in Mod. Phys. Lett.

Modular Invariance of Finite Size Corrections and a Vortex Critical Phase

We analyze a continuous spin Gaussian model on a toroidal triangular lattice with periods $L_0$ and $L_1$ where the spins carry a representation of the fundamental group of the torus labeled by phases $u_0$ and $u_1$. We find the {\it exact finite size and lattice corrections}, to the partition function $Z$, for arbitrary mass $m$ and phases $u_i$. Summing $Z^{-1/2}$ over phases gives the corresponding result for the Ising model. The limits $m\rightarrow0$ and $u_i\rightarrow0$ do not commute. With $m=0$ the model exhibits a {\it vortex critical phase} when at least one of the $u_i$ is non-zero. In the continuum or scaling limit, for arbitrary $m$, the finite size corrections to $-\ln Z$ are {\it modular invariant} and for the critical phase are given by elliptic theta functions. In the cylinder limit $L_1\rightarrow\infty$ the ``cylinder charge'' $c(u_0,m^2L_0^2)$ is a non-monotonic function of $m$ that ranges from $2(1+6u_0(u_0-1))$ for $m=0$ to zero for $m\rightarrow\infty$.Comment: 12 pages of Plain TeX with two postscript figure insertions called torusfg1.ps and torusfg2.ps which can be obtained upon request from [email protected]