Spin and energy correlations in the one dimensional spin 1/2 Heisenberg model

In this paper, we study the spin and energy dynamic correlations of the one dimensional spin 1/2 Heisenberg model, using mostly exact diagonalization numerical techniques. In particular, observing that the uniform spin and energy currents decay to finite values at long times, we argue for the absence of spin and energy diffusion in the easy plane anisotropic Heisenberg model.Comment: 10 pages, 3 figures, gzipped postscrip

Hard hexagon partition function for complex fugacity

We study the analyticity of the partition function of the hard hexagon model in the complex fugacity plane by computing zeros and transfer matrix eigenvalues for large finite size systems. We find that the partition function per site computed by Baxter in the thermodynamic limit for positive real values of the fugacity is not sufficient to describe the analyticity in the full complex fugacity plane. We also obtain a new algebraic equation for the low density partition function per site.Comment: 49 pages, IoP styles files, lots of figures (png mostly) so using PDFLaTeX. Some minor changes added to version 2 in response to referee report

Integrability vs non-integrability: Hard hexagons and hard squares compared

In this paper we compare the integrable hard hexagon model with the non-integrable hard squares model by means of partition function roots and transfer matrix eigenvalues. We consider partition functions for toroidal, cylindrical, and free-free boundary conditions up to sizes $40\times40$ and transfer matrices up to 30 sites. For all boundary conditions the hard squares roots are seen to lie in a bounded area of the complex fugacity plane along with the universal hard core line segment on the negative real fugacity axis. The density of roots on this line segment matches the derivative of the phase difference between the eigenvalues of largest (and equal) moduli and exhibits much greater structure than the corresponding density of hard hexagons. We also study the special point $z=-1$ of hard squares where all eigenvalues have unit modulus, and we give several conjectures for the value at $z=-1$ of the partition functions.Comment: 46 page

Randomly incomplete spectra and intermediate statistics

By randomly removing a fraction of levels from a given spectrum a model is constructed that describes a crossover from this spectrum to a Poisson spectrum. The formalism is applied to the transitions towards Poisson from random matrix theory (RMT) spectra and picket fence spectra. It is shown that the Fredholm determinant formalism of RMT extends naturally to describe incomplete RMT spectra.Comment: 9 pages, 2 figures. To appear in Physical Review

High-precision estimate of g4 in the 2D Ising model

We compute the renormalized four-point coupling in the 2d Ising model using transfer-matrix techniques. We greatly reduce the systematic uncertainties which usually affect this type of calculations by using the exact knowledge of several terms in the scaling function of the free energy. Our final result is g4=14.69735(3).Comment: 17 pages, revised version with minor changes, accepted for publication in Journal of Physics

Reconsidering data in learning analytics: opportunities for critical research using a documentation studies framework

In this article, we argue that the contributions of documentation studies can provide a useful framework for analyzing the datafication of students due to emerging learning analytics (LA) practices. Specifically, the concepts of individuals being ‘made into’ data and how that data is ‘considered as’ can help to frame vital questions concerning the use of student data in LA. More specifically, approaches informed by documentation studies will enable researchers to address the sociotechnical processes underlying how students are constructed into data, and ways data about students are considered and understood. We draw on these concepts to identify and describe three areas for future research in LA. With the description of each area, we provide a brief analysis of current practices in American higher education, highlighting how documentation studies enables deeper analytical digging

Painlev\'e Transcendent Describes Quantum Correlation Function of the XXZ Antiferromagnet away from the free-fermion point

We consider quantum correlation functions of the antiferromagnetic spin-$\frac{1}{2}$ Heisenberg XXZ spin chain in a magnetic field. We show that for a magnetic field close to the critical field $h_c$ (for the critical magnetic field the ground state is ferromagnetic) certain correlation functions can be expressed in terms of the solution of the Painlev\'e V transcendent. This establishes a relation between solutions of Painlev\'e differential equations and quantum correlation functions in models of {\sl interacting} fermions. Painlev\'e transcendents were known to describe correlation functions in models with free fermionic spectra.Comment: 10 pages, LaTeX2

Dynamic wetting with two competing adsorbates

We study the dynamic properties of a model for wetting with two competing adsorbates on a planar substrate. The two species of particles have identical properties and repel each other. Starting with a flat interface one observes the formation of homogeneous droplets of the respective type separated by nonwet regions where the interface remains pinned. The wet phase is characterized by slow coarsening of competing droplets. Moreover, in 2+1 dimensions an additional line of continuous phase transition emerges in the bound phase, which separates an unordered phase from an ordered one. The symmetry under interchange of the particle types is spontaneously broken in this region and finite systems exhibit two metastable states, each dominated by one of the species. The critical properties of this transition are analyzed by numeric simulations.Comment: 11 pages, 12 figures, final version published in PR

SCOZA for Monolayer Films

We show the way in which the self-consistent Ornstein-Zernike approach (SCOZA) to obtaining structure factors and thermodynamics for Hamiltonian models can best be applied to two-dimensional systems such as thin films. We use the nearest-neighbor lattice gas on a square lattice as an illustrative example.Comment: 10 pages, 5 figure

Caffeine Intake During Pregnancy and Weight of Offspring in Childhood: A Systematic Review

Background: Childhood obesity currently affects one third of the United States’ youth. Meeting criteria for overweight and obesity in childhood not only increases the risk of being overweight or obese in adulthood, but also increases the risk of comorbidities of obesity including: type 2 diabetes, metabolic syndrome, non-alcoholic steatohepatitis, hypertension, obstructive sleep apnea, and slipped capital femoral epiphysis. Several factors have been implicated to have a causal relationship or association with excessive weight gain; however, new studies are suggesting that a significant influence on the weight of the child is present in-utero. The current review explores the relationship between caffeine consumption during pregnancy and the weight of offspring in childhood. The purpose of this review is to organize and critically appraise the current data in order to realign our standard of care with the most recent information. Preventing childhood obesity is our best line of defense for our children and the health of our nation. Method: A comprehensive search of MEDLINE-PubMed, Web of Science, CINAHL-EBSCO, and MEDLINE-Ovid was conducted using the following key words: maternal, pregnant women, caffeine, and childhood obesity. The search produced five articles of which four were relevant to the topic and met all eligibility criteria. The four applicable articles were then reviewed using GRADE criteria. Results: Three of the 4 eligible studies suggest that there is an association between higher levels of caffeine intake in pregnancy and increased weight in childhood compared to lower levels of maternal caffeine intake. One study even suggests complete avoidance of caffeine may be advisable after findings reveal increased BMI from infancy to childhood were associated with any amount of caffeine intake during pregnancy. In contrast, a study by the Research Institute at Nationwide Children’s Hospital did not support the theory that increasing maternal caffeine consumption during pregnancy increases the risk of childhood obesity. Conclusion: The use of caffeine during pregnancy may be linked to childhood obesity. Providers should consider giving stricter recommendations than the current ACOG guidelines of \u3c200mg/day and may even educate pregnant mothers to eliminate caffeine altogether. Keywords: Maternal, pregnant women, caffeine, childhood obesit